On the symmetric positive solutions of nonlinear fourth order ordinary differential equations with four-point boundary value conditions: a fixed point theory approach

The Journal of Nonlinear Sciences and its Applications

article

Asaduzzaman¹  Zulfikar Ali² 

[1] Department of Mathematics, Islamic University;Department of Mathematics, University of Rajshahi

关键词: Fourth order four-point boundary value problem;    existence of symmetric positive solution;    Krasnoselskii's fixed point theorem;    Green's function;   

DOI  :  10.22436/jnsa.013.06.06

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

The purpose of this paper is to investigate the existence of symmetric positive solutions of the following nonlinear fourth order system of ordinary differential equations\[\begin{cases}-u^{(4)}(t) = f(t,\, v),\\-v^{(4)}(t) = g(t,\, u) , \,\,\,t\in[0,\,1],\end{cases}\]with the four-point boundary value conditions\[\begin{cases}u(t) = u(1-t),\,\, u^{\prime\prime\prime}(0)-u^{\prime\prime\prime}(1)=u^{\prime\prime}(t_{1})+u^{\prime\prime}(t_{2}),\\v(t) = v(1-t),\,\, v^{\prime\prime\prime}(0)-v^{\prime\prime\prime}(1)=v^{\prime\prime}(t_{1})+v^{\prime\prime}(t_{2}), \,\,\,0

【 授权许可】

Unknown