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Applicable Analysis
An International Journal
Volume 35, 1990 - Issue 1-4
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Original Articles

Existence of solutions for nonlinear singular boundary value problems

L. E. Bobisud Department of Mathematics and Statistics, University of Idaho, Moscow, Idaho, 83843
Pages 43-57 | Published online: 02 May 2007

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Vivek, Manoj Kumar & S. N. Mishra. (2023) Solution of linear and nonlinear singular value problems using operational matrix of integration of Taylor wavelets. Journal of Taibah University for Science 17:1.
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Donal O'Regan. (1993) Positive solutions to singular boundary value problems with at most linear growth. Applicable Analysis 49:3-4, pages 171-196.
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Articles from other publishers (64)

Khalid K. Ali, M.S. Mehanna, Abdul-Majid Wazwaz & M.A. Shaalan. (2024) Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method. Partial Differential Equations in Applied Mathematics 10, pages 100676.
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Julee Shahni & Randhir Singh. (2024) Numerical solution and error analysis of the Thomas–Fermi type equations with integral boundary conditions by the modified collocation techniques. Journal of Computational and Applied Mathematics 441, pages 115701.
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Vivek & Manoj Kumar. (2024) Solution of linear and nonlinear singular value problems using operational matrix of integration of Fibonacci wavelets. Journal of Engineering Mathematics 145:1.
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Shabanam Kumari, Arvind Kumar Singh & Utsav Gupta. (2024) Collocation Technique Based on Chebyshev Polynomials to Solve Emden–Fowler-Type Singular Boundary Value Problems with Derivative Dependence. Mathematics 12:4, pages 592.
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Maheshwar Pathak & Pratibha Joshi. (2023) Quasilinear bessel polynomial collocation method for the solutions of nonlinear singular boundary value problems. International Journal of Modern Physics C 35:02.
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Pradip Roul, V. M. K. Prasad Goura & Ravi Agarwal. (2023) An optimal computational method for a general class of nonlinear boundary value problems. Journal of Mathematical Chemistry 61:9, pages 1842-1878.
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Mohammad Prawesh Alam & Arshad Khan. (2023) A high-order numerical method for solving nonlinear derivative-dependent singular boundary value problems using trigonometric B-spline basis function. Mathematical Sciences.
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Khalid K. Ali, M.S. Mehanna, M. Ismail Abdelrahman & M.A. Shaalan. (2022) Analytical and Numerical solutions for fourth order Lane–Emden–Fowler equation. Partial Differential Equations in Applied Mathematics 6, pages 100430.
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Sheerin Kayenat & Amit Kumar Verma. (2022) On the choice of denominator functions and convergence of NSFD schemes for a class of nonlinear SBVPs. Mathematics and Computers in Simulation 200, pages 263-284.
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Julee Shahni & Randhir Singh. (2021) A fast numerical algorithm based on Chebyshev-wavelet technique for solving Thomas-Fermi type equation. Engineering with Computers 38:S4, pages 3409-3422.
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Julee Shahni & Randhir Singh. (2021) Laguerre wavelet method for solving Thomas–Fermi type equations. Engineering with Computers 38:4, pages 2925-2935.
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Julee Shahni & Randhir Singh. (2022) Numerical simulation of Emden–Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet and Laguerre-wavelet collocation methods. Mathematics and Computers in Simulation 194, pages 430-444.
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Randhir Singh & Abdul-Majid Wazwaz. (2022) An Efficient Method for Solving the Generalized Thomas–Fermi and Lane–Emden–Fowler Type Equations with Nonlocal Integral Type Boundary Conditions. International Journal of Applied and Computational Mathematics 8:2.
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Julee Shahni & Randhir Singh. (2020) Numerical results of Emden–Fowler boundary value problems with derivative dependence using the Bernstein collocation method. Engineering with Computers 38:S1, pages 371-380.
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Pradip Roul & V.M.K. Prasad Goura. (2022) A superconvergent B-spline technique for second order nonlinear boundary value problems. Applied Mathematics and Computation 414, pages 126615.
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Randhir Singh & Abdul-Majid Wazwaz. (2021) Analytical approximations of three-point generalized Thomas–Fermi and Lane–Emden–Fowler type equations. The European Physical Journal Plus 137:1.
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Agnieszka Kałamajska & Anna Maria Kosiorek. (2020) On maximum principles for solutions to nonlinear elliptic ODEs and radial solutions to nonlinear elliptic PDE's via Opial‐type inequalities. Mathematical Methods in the Applied Sciences 44:6, pages 4616-4635.
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Ujwal Warbhe. An eficient algorithm for solving a class of derivative dependent nonlinear doubly singular boundary value problems. An eficient algorithm for solving a class of derivative dependent nonlinear doubly singular boundary value problems.
Pradip Roul & V. M. K. Prasad Goura. (2020) Numerical solution of doubly singular boundary value problems by finite difference method. Computational and Applied Mathematics 39:4.
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Randhir Singh, Vandana Guleria & Mehakpreet Singh. (2020) Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations. Mathematics and Computers in Simulation 174, pages 123-133.
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Amit K. Verma, Biswajit Pandit, Lajja Verma & Ravi P. Agarwal. (2020) A Review on a Class of Second Order Nonlinear Singular BVPs. Mathematics 8:7, pages 1045.
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Julee Shahni & Randhir Singh. (2020) An efficient numerical technique for Lane–Emden–Fowler boundary value problems: Bernstein collocation method. The European Physical Journal Plus 135:6.
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Amit K. Barnwal & Priti Pathak. (2019) Successive iteration technique for singular nonlinear system with four-point boundary conditions. Journal of Applied Mathematics and Computing 62:1-2, pages 301-324.
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Randhir Singh. (2019) Analytic solution of singular Emden-Fowler-type equations by Green’s function and homotopy analysis method. The European Physical Journal Plus 134:11.
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Pradip Roul, V.M.K. Prasad Goura & Ravi Agarwal. (2019) A new high order numerical approach for a class of nonlinear derivative dependent singular boundary value problems. Applied Numerical Mathematics 145, pages 315-341.
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Pradip Roul. (2018) Doubly singular boundary value problems with derivative dependent source function: A fast‐converging iterative approach. Mathematical Methods in the Applied Sciences 42:1, pages 354-374.
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Pradip Roul & V.M.K. Prasad Goura. (2019) B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems. Applied Mathematics and Computation 341, pages 428-450.
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Pradip Roul. (2016) An improved iterative technique for solving nonlinear doubly singular two-point boundary value problems. The European Physical Journal Plus 131:6.
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Pradip Roul & Ujwal Warbhe. (2016) A novel numerical approach and its convergence for numerical solution of nonlinear doubly singular boundary value problems. Journal of Computational and Applied Mathematics 296, pages 661-676.
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Randhir Singh, Jitendra Kumar & Gnaneshwar Nelakanti. (2013) Approximate series solution of singular boundary value problems with derivative dependence using Green’s function technique. Computational and Applied Mathematics 33:2, pages 451-467.
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Randhir Singh & Jitendra Kumar. (2013) The Adomian decomposition method with Green’s function for solving nonlinear singular boundary value problems. Journal of Applied Mathematics and Computing 44:1-2, pages 397-416.
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Randhir Singh, Jitendra Kumar & Gnaneshwar Nelakanti. (2012) New Approach for Solving a Class of Doubly Singular Two-Point Boundary Value Problems Using Adomian Decomposition Method. Advances in Numerical Analysis 2012, pages 1-22.
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R. K. Pandey & G. K. Gupta. (2012) A Note on Fourth Order Method for Doubly Singular Boundary Value Problems. Advances in Numerical Analysis 2012, pages 1-21.
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Amit K. Verma, Ravi P. Agarwal & Lajja Verma. (2012) Bessel functions and singular BVPs arising in physiology in the presence of upper and lower solutions in reverse order. Journal of Applied Mathematics and Computing 39:1-2, pages 445-457.
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R. K. Pandey & A. K. Barnwal. (2012) Multiple Solutions for Nonlinear Doubly Singular Three-Point Boundary Value Problems with Derivative Dependence. International Journal of Differential Equations 2012, pages 1-21.
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Amit K. Verma. (2011) The monotone iterative method and zeros of Bessel functions for nonlinear singular derivative dependent BVP in the presence of upper and lower solutions. Nonlinear Analysis: Theory, Methods & Applications 74:14, pages 4709-4717.
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R. K. Pandey & Amit K. Verma. (2011) On a Constructive Approach for Derivative-Dependent Singular Boundary Value Problems. International Journal of Differential Equations 2011, pages 1-16.
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Naseer Ahmad Asif, Paul W. Eloe & Rahmat Ali Khan. (2010) POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS. Journal of the Korean Mathematical Society 47:5, pages 985-1000.
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R. K. Pandey & Amit K. Verma. (2009) On solvability of derivative dependent doubly singular boundary value problems. Journal of Applied Mathematics and Computing 33:1-2, pages 489-511.
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R.K. Pandey & Amit K. Verma. (2010) Monotone method for singular BVP in the presence of upper and lower solutions. Applied Mathematics and Computation 215:11, pages 3860-3867.
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R.K. Pandey & A.K. Verma. (2009) A note on existence-uniqueness results for a class of doubly singular boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 71:7-8, pages 3477-3487.
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Bao Qiang Yan, Donal O’regan & Ravi P. Agarwal. (2006) Positive Solutions to Singular Boundary Value Problems with Sign Changing Nonlinearities on the Half-Line via Upper and Lower Solutions. Acta Mathematica Sinica, English Series 23:8, pages 1447-1456.
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Bingmei Liu, Lishan Liu & Yonghong Wu. (2007) Positive solutions for singular systems of three-point boundary value problems. Computers & Mathematics with Applications 53:9, pages 1429-1438.
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Lishan Liu, Bingmei Liu & Yonghong Wu. (2007) Positive solutions of singular boundary value problems for nonlinear differential systems. Applied Mathematics and Computation 186:2, pages 1163-1172.
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Baoqiang Yan, Donal O’Regan & Ravi P. Agarwal. (2007) Multiple positive solutions for singular problems with mixed boundary data and derivative dependence. Mathematical and Computer Modelling 45:3-4, pages 404-430.
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Donal O'Regan, Baoqiang Yan & Ravi P. Agarwal. (2006) Nonlinear Boundary Value Problems on Semi-Infinite Intervals using Weighted Spaces: An Upper and Lower Solution Approach. Positivity 11:1, pages 171-189.
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Baoqiang Yan, Donal O’Regan & Ravi P. Agarwal. (2006) Unbounded solutions for singular boundary value problems on the semi-infinite interval: Upper and lower solutions and multiplicity. Journal of Computational and Applied Mathematics 197:2, pages 365-386.
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YUJI LIU & WEIGAO GE. (2011) EXISTENCE THEOREMS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS. Analysis and Applications 02:01, pages 71-85.
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Baoqiang Yan & Yansheng Liu. (2004) Unbounded solutions of the singular boundary value problems for second order differential equations on the half-line. Applied Mathematics and Computation 147:3, pages 629-644.
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Petio Kelevedjiev. (1999) Nonnegative solutions to some singular second-order boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 36:4, pages 481-494.
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Junyu Wang. (1995) Solvability of singular nonlinear two-point boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 24:4, pages 555-561.
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Donal O'regan. (1994) Positive solutions for a class of boundary value problems on infinite intervals. Nonlinear Differential Equations and Applications NoDEA 1:3, pages 203-228.
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Donal O'Regan. (1994) Nonresonance and existence for singular boundary-value problems. Nonlinear Analysis: Theory, Methods & Applications 23:2, pages 165-186.
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D. O'Regan. (1994) Positive solutions to certain classes of singular nonlinear second order boundary value problems. Periodica Mathematica Hungarica 28:2, pages 151-171.
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Yong Zhang. (1993) Existence of solutions of a kind of singular boundary value problem. Nonlinear Analysis: Theory, Methods & Applications 21:2, pages 153-159.
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Dónal O'Regan. (1993) Nonlinear systems of two point boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 20:8, pages 979-991.
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Donal O'Regan. (1993) Singular sturm liouville problems and existence of solutions to singular nonlinear boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 20:7, pages 767-779.
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P. W. Eloe & J. Henderson. (2006) Existence of Solutions for Some Singular Higher Order Boundary Value Problems. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 73:11, pages 315-323.
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Donal O'Regan. (1992) Existence theorems for certain classes of singular boundary value problems. Journal of Mathematical Analysis and Applications 168:2, pages 523-539.
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L.E Bobisud. (1992) Existence of solutions to some nonlinear diffusion problems. Journal of Mathematical Analysis and Applications 168:2, pages 413-424.
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Dónal O'Regan. (1992) Some existence principles and some general results for singular nonlinear two point boundary value problems. Journal of Mathematical Analysis and Applications 166:1, pages 24-40.
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L.E Bobisud & Y.S Lee. (1991) Existence of monotone or positive solutions of singular second-order sublinear differential equations. Journal of Mathematical Analysis and Applications 159:2, pages 449-468.
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