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Existence of solutions for a fully nonlinear fourth-order two-point boundary value problem

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Abstract

In this paper, we investigate the existence of solutions of a fully nonlinear fourth-order differential equation

$$x^{(4)}=f(t,x,x',x'',x'''),\quad t\in [0,1]$$

with one of the following sets of boundary value conditions;

$$x'(0)=x(1)=a_{0}x''(0)-b_{0}x'''(0)=a_{1}x''(1)+b_{1}x'''(1)=0,$$
$$x(0)=x'(1)=a_{0}x''(0)-b_{0}x'''(0)=a_{1}x''(1)+b_{1}x'''(1)=0.$$

By using the Leray-Schauder degree theory, the existence of solutions for the above boundary value problems are obtained. Meanwhile, as an application of our results, an example is given.

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Authors and Affiliations

  1. Department of Mathematics, Beihua University, JiLin City, 132013, P.R. China

    Minghe Pei

  2. Department of Mathematics, Yeungnam University, Kyongsan, 712-749, South Korea

    Sung Kag Chang

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  1. Minghe Pei
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  2. Sung Kag Chang
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Correspondence to Sung Kag Chang.

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Pei, M., Chang, S.K. Existence of solutions for a fully nonlinear fourth-order two-point boundary value problem. J. Appl. Math. Comput. 37, 287–295 (2011). https://doi.org/10.1007/s12190-010-0434-3

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  • DOI: https://doi.org/10.1007/s12190-010-0434-3

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