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Applicable Analysis
An International Journal
Volume 74, 2000 - Issue 1-2
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Original Articles

Existnence and nonexistence of positive solutions of fourth order nonlinear boundary value problems

John.R Graef Department of Mathematics, University of Tennesse At Chattanooga, Chattanooga, TN, 37403 E-mail: [email protected]
&
Bo Yang Department Of Mathematics And Statistics, Mississippi State Universtiy, Mississippi State MS, 39762 E-mail: by2@ra. msstate.edu
Pages 201-214 | Received 01 Jul 1999, Published online: 02 May 2007

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Jingjing Wang, Chenghua Gao & Yanqiong Lu. (2023) Global structure of positive solutions for semipositone nonlinear Euler-Bernoulli beam equation with Neumann boundary conditions. Quaestiones Mathematicae 46:4, pages 641-669.
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Shapour Heidarkhani, Ghasem A. Afrouzi, Massimiliano Ferrara & Shahin Moradi. (2016) Variational approaches to impulsive elastic beam equations of Kirchhoff type. Complex Variables and Elliptic Equations 61:7, pages 931-968.
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Liu Yuji & Ge Weigao. (2003) Double Positive Solutions of Fourth-Order Nonlinear Boundary Value Problems. Applicable Analysis 82:4, pages 369-380.
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John R. Graff & Bo Yang. (2001) Boundary value problems for 2n-th order nonlinear ordinary differential equation. Applicable Analysis 79:3-4, pages 503-517.
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Articles from other publishers (29)

John R. Graef & Bo Yang. (2023) Positive solutions for a fourth-order p -Laplacian boundary value problem . Georgian Mathematical Journal 30:5, pages 703-711.
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Jingjing Wang, Chenghua Gao & Xingyue He. (2023) Green’s Function and Existence Results for Solutions of Semipositone Nonlinear Euler–Bernoulli Beam Equations with Neumann Boundary Conditions. Mathematical Notes 113:3-4, pages 574-583.
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Jingjing Wang, Chenghua Gao & Xingyue He. (2022) A monotone iteration for a nonlinear Euler-Bernoulli beam equation with indefinite weight and Neumann boundary conditions. Open Mathematics 20:1, pages 1594-1609.
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Ghasem A. Afrouzi, Shahin Moradi & Giuseppe Caristi. (2017) Infinitely Many Solutions for Impulsive Nonlocal Elastic Beam Equations. Differential Equations and Dynamical Systems 30:2, pages 287-300.
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Slimane Benaicha & Faouzi Haddouchi. (2016) Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem. Annals of West University of Timisoara - Mathematics and Computer Science 54:1, pages 73-86.
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Massimiliano Ferrara, Giuseppe Caristi & Amjad Salari. (2016) Existence of Infinitely Many Periodic Solutions for Perturbed Semilinear Fourth-Order Impulsive Differential Inclusions. Abstract and Applied Analysis 2016, pages 1-12.
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Yaling Zhou & XueMei Zhang. (2015) New existence theory of positive solutions to fourth order p-Laplacian elasticity problems. Boundary Value Problems 2015:1.
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Ruikuan Liu & Ruyun Ma. (2014) Existence of Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions. Journal of Applied Mathematics 2014, pages 1-5.
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John R. Graef, Lingju Kong & Bo Yang. (2012) Positive solutions of boundary value problems for discrete and continuous beam equations. Journal of Applied Mathematics and Computing 41:1-2, pages 197-208.
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Qingliu Yao. (2013) Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem. Applications of Mathematics 58:1, pages 93-110.
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Yongping Sun, Xiaoping Zhang & Min Zhao. (2013) Successive Iteration of Positive Solutions for Fourth-Order Two-Point Boundary Value Problems. Abstract and Applied Analysis 2013, pages 1-8.
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Gennaro Infante & Paolamaria Pietramala. 2013. Differential and Difference Equations with Applications. Differential and Difference Equations with Applications 429 437 .
Maher Berzig & Bessem Samet. (2012) Positive solutions to periodic boundary value problems involving nonlinear operators of Meir-Keeler-type. Rendiconti del Circolo Matematico di Palermo 61:2, pages 279-296.
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Bo Yang. (2011) Upper and lower estimates for positive solutions of the higher order Lidstone boundary value problem. Journal of Mathematical Analysis and Applications 382:1, pages 290-302.
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Yong-ping Sun. (2011) Existence and multiplicity of positive solutions for an elastic beam equation. Applied Mathematics-A Journal of Chinese Universities 26:3, pages 253-264.
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Qingliu Yao. (2008) Successively Iterative Technique of a Classical Elastic Beam Equation with Carathéodory Nonlinearity. Acta Applicandae Mathematicae 108:2, pages 385-394.
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Xiaoping Zhang. (2009) Existence and iteration of monotone positive solutions for an elastic beam equation with a corner. Nonlinear Analysis: Real World Applications 10:4, pages 2097-2103.
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Fu-Hsiang Wong, Sheng-Ping Wang, Shiueh-Ling Yu & Wei-Cheng Lian. (2009) Existence of positive solutions for an -order nonlinear BVP . Computers & Mathematics with Applications 58:3, pages 498-507.
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Shiueh-Ling Yu, Fu-Hsiang Wong, Cheh-Chih Yeh & Shang-Wen Lin. (2007) Existence of positive solutions for order -Laplacian BVP . Computers & Mathematics with Applications 53:9, pages 1367-1379.
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De-xiang Ma, Yu Tian & Wei-gao Ge. (2006) EXISTENCE THEOREMS OF POSITIVE SOLUTIONS FOR A FOURTH-ORDER THREE-POINT BOUNDARY VALUE PROBLEM. Taiwanese Journal of Mathematics 10:6.
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Yuji Liu. (2006) Solutions of two-point boundary value problems for even-order differential equations. Journal of Mathematical Analysis and Applications 323:1, pages 721-740.
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Binggen Zhang & Yuji Liu. (2006) Solutions of Boundary Value Problems for $2n$-Order Differential Equations. Rocky Mountain Journal of Mathematics 36:5.
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Jun Ji & Bo Yang. (2006) Eigenvalue comparisons for boundary value problems of the discrete beam equation. Advances in Difference Equations 2006, pages 1-10.
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Yuji Liu, Pinghua Yang & Weigao Ge. (2005) Solutions of two-point BVPs at resonance for higher order impulsive differential equations. Nonlinear Analysis: Theory, Methods & Applications 60:5, pages 887-923.
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Yuji Liu & Weigao Ge. (2005) Positive solutions of two-point boundary value problems for -order differential equations dependent on all derivatives . Applied Mathematics Letters 18:2, pages 209-218.
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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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John R. Graef, Chuanxi Qian & Bo Yang. (2003) A three point boundary value problem for nonlinear fourth order differential equations. Journal of Mathematical Analysis and Applications 287:1, pages 217-233.
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Guoliang Shi & Shaozhu Chen. (2003) Positive solutions of even higher-order singular superlinear boundary value problems. Computers & Mathematics with Applications 45:4-5, pages 593-603.
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Guoliang Shi & Shaozhu Chen. (2009) Positive solutions of fourth-order superlinear singular boundary value problems. Bulletin of the Australian Mathematical Society 66:1, pages 95-104.
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