The unique symmetric positive solutions for nonlinear fourth order arbitrary two-point boundary value problems: A fixed point theory approach

admin December 22, 2018

Authors:

Md. Asaduzzaman,Md. Zulfikar Ali,

DOI NO:

https://doi.org/10.26782/jmcms.2018.12.00017

Keywords:

Arbitrary two-pointboundary conditions,Nonlinear fourthorder ordinary differential equation,Unique symmetric positive solutions,Fixed point theorem,

Abstract

In this paper, we explore the existence and uniqueness of positive solutions for the following nonlinear fourth order ordinary differential equation        (4) u t  f t,u t , t a, b , withthe following arbitrary two-point boundary conditions: ua  ub  ua  ub  0, where, a, b are two arbitrary constants satisfying b  0, a 1 b and f Ca,b0,,0,.Here we also demonstrate that under certain assumptions the above boundary value problem exist a unique symmetric positive solution. The analysis of this paper is based on a fixed point theorem in partially ordered metric spaces due to Amini-Harandi and Emami. The results of this paper generalize the results of several authors in literature. Finally, we provide some illustrative examples to support our analytic proof.

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Author(s): Md. Asaduzzaman, Md. Zulfikar Ali View Download