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Applicable Analysis
An International Journal
Volume 36, 1990 - Issue 3-4
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Original Articles

Existence and uniqueness theorems for some fourth order fully quasilinear boundary value problems

Chaitan P. Gupta Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 60439-4801
Pages 157-169 | Received 06 Sep 1989, Published online: 02 May 2007

Citations (33)

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Read on this site (4)

Ma Ruyun & Wang Haiyan. (1995) On the existence of positive solutions of fourth-order ordinary differential equations. Applicable Analysis 59:1-4, pages 225-231.
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Martin Senkyrík. (1995) Fourth order boundary value problems and nonlinear beams. Applicable Analysis 59:1-4, pages 15-25.
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Chaitan P. Gupta. (1995) A sharp conditon for existence of a solution for a fourth order boundary value problem. Applicable Analysis 56:1-2, pages 289-304.
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Bonanno Gabriele & Salvatore A. Marano. (1994) A remark on some existence and uniqueness theorems for a fourth order boundary value problem. Applicable Analysis 55:3-4, pages 185-187.
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Articles from other publishers (29)

Dmitry M. Polyakov. (2023) Eigenvalue Asymptotics and a Trace Formula for a Fourth-Order Differential Operator. Complex Analysis and Operator Theory 17:8.
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D. M Polyakov. (2023) O spektral'nykh svoystvakh samosopryazhennogo operatora chetvertogo poryadka. Дифференциальные уравнения 59:2, pages 164-169.
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D. M. Polyakov. (2023) On the Spectral Properties of a Fourth-Order Self-Adjoint Operator. Differential Equations 59:2, pages 168-173.
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Belkacem Chaouchi & Marko Kostić. (2022) On the solvability of a fourth-order differential evolution equation on singular cylindrical domain in R 4 . Mathematica Slovaca 72:4, pages 911-924.
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B. Kovács. (2021) Existence of Positive Solution for a Singular Fourth–Order Differential System. Acta Marisiensis. Seria Technologica 18:2, pages 47-60.
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Mahboub Baccouch. (2020) Analysis of optimal superconvergence of the local discontinuous Galerkin method for nonlinear fourth-order boundary value problems. Numerical Algorithms 86:4, pages 1615-1650.
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Bingzhi Sun & Weihua Jiang. (2020) Existence of solutions for functional boundary value problems at resonance on the half-line. Boundary Value Problems 2020:1.
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Mahboub Baccouch. (2019) A Superconvergent Local Discontinuous Galerkin Method for Nonlinear Fourth-Order Boundary-Value Problems. International Journal of Computational Methods 17:07, pages 1950035.
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Ravi P. Agarwal, B. Kovacs & D. O’Regan. (2013) Existence of positive solution for a sixth–order differential system with variable parameters. Journal of Applied Mathematics and Computing 44:1-2, pages 437-454.
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Ruyun Ma, Haiyan Wang & Mohammed Elsanosi. (2013) Spectrum of a linear fourth‐order differential operator and its applications. Mathematische Nachrichten 286:17-18, pages 1805-1819.
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J. Caballero, J. Harjani & K. Sadarangani. (2011) Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems. Abstract and Applied Analysis 2011, pages 1-13.
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J. Harjani & K. Sadarangani. (2010) Existence and uniqueness of positive solutions for a nonlinear fourth-order boundary value problem. Positivity 14:4, pages 849-858.
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Changchun Yu, Shihua Chen, Francis Austin & Jinhu Lü. (2010) Positive solutions of four-point boundary value problem for fourth order ordinary differential equation. Mathematical and Computer Modelling 52:1-2, pages 200-206.
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Huanmin Yao & Minggen Cui. (2010) Searching the least value method for solving fourth-order nonlinear boundary value problems. Computers & Mathematics with Applications 59:2, pages 677-683.
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Xuemei Zhang & Weigao Ge. (2009) Positive solutions for a class of boundary-value problems with integral boundary conditions. Computers & Mathematics with Applications 58:2, pages 203-215.
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Shenghuai Huang & Zhan Zhou. (2009) On the Nonexistence and Existence of Solutions for a Fourth-Order Discrete Boundary Value Problem. Advances in Difference Equations 2009, pages 1-18.
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De-xiang Ma & Xiao-zhong Yang. (2009) Upper and lower solution method for fourth-order four-point boundary value problems. Journal of Computational and Applied Mathematics 223:2, pages 543-551.
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Yongli Zhong, Shihua Chen & Changping Wang. (2008) Existence results for a fourth-order ordinary differential equation with a four-point boundary condition. Applied Mathematics Letters 21:5, pages 465-470.
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S. Weng, H. Gao, D. Jiang & X. Hou. (2008) Upper and Lower Solutions Method for Fourth-Order Periodic Boundary Value Problems. Journal of Applied Analysis 14:1.
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De-Xiang Ma & Wei-Gao Ge. (2006) Multiple symmetric positive solutions of fourth-order two point boundary value problem. Journal of Applied Mathematics and Computing 22:1-2, pages 295-306.
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Zhao-Cai Hao & Lokenath Debnath. (2005) On eigenvalue intervals and eigenfunctions of fourth-order singular boundary value problems. Applied Mathematics Letters 18:5, pages 543-553.
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Daqing Jiang, Huizhao Liu & Xiaojie Xu. (2005) Nonresonant singular fourth-order boundary value problems. Applied Mathematics Letters 18:1, pages 69-75.
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B. Liu. (2004) Positive solutions of fourth-order two point boundary value problems. Applied Mathematics and Computation 148:2, pages 407-420.
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Daqing Jiang, Wenjie Gao & Aying Wan. (2002) A monotone method for constructing extremal solutions to fourth-order periodic boundary value problems. Applied Mathematics and Computation 132:2-3, pages 411-421.
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Ruyun Ma. (2000) Positive Solutions for Semipositone (k,n−k) Conjugate Boundary Value Problems. Journal of Mathematical Analysis and Applications 252:1, pages 220-229.
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Ma Ruyun, Zhang Jihui & Fu Shengmao. (1997) The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems. Journal of Mathematical Analysis and Applications 215:2, pages 415-422.
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Ma Ruyun & Ma Qinsheng. (1995) Multiplicity results for a fourth-order boundary value problem. Applied Mathematics and Mechanics 16:10, pages 961-969.
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D. D. Hai. (1995) Boundary value problems for fourth order differential equations in Hilbert space. Rendiconti del Circolo Matematico di Palermo 44:2, pages 197-214.
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Ravi P. Agarwal & Peter Y. H. PangRavi P. Agarwal & Peter Y. H. Pang. 1995. Opial Inequalities with Applications in Differential and Difference Equations. Opial Inequalities with Applications in Differential and Difference Equations 356 389 .

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