Existence of nontrivial solutions for a nonlinear fourth-order boundary value problem via iterative method

Volume 9, Issue 6, pp 4295--4304 http://dx.doi.org/10.22436/jnsa.009.06.71

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Authors

Chengbo Zhai - School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P. R. China. Chunrong Jiang - School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P. R. China.

Abstract

In this article, we study a nonlinear fourth-order differential equation two-point boundary value problem. We use monotone iterative technique and lower and upper solutions of completely continuous operators to get the existence of nontrivial solutions for the problem. The results can guarantee the existence of nontrivial sign-changing solutions and positive solutions, and we can construct two iterative sequences for approximating them. Finally, two examples are given to illustrate the main results.

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Keywords

• Existence of solutions
• fourth-order boundary value problem
• iterative method
• lower and upper solutions.

MSC

•  34B18
•  34B15

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