Abstract
The aim of this paper is to study the more accurate existence results of positive solution for a nonlinear fourth order ordinary differential equation (for short NLFOODE) using four-point boundary value conditions (for short BVCs). The upper and lower solution method and Schauder’s fixed point theorem have been applied to demonstrate the obtained existence results. First, the Green’s function of the corresponding linear boundary value problem (for short BVP) has been constructed and then it is used to solve the considered BVP of this paper. An example has also been included at the end of this paper to support the analytic proof.
Highlights
IntroductionIt is well established that the xed point technique and upper and lower solution method are most important techniques for checking the existence of positive solutions of ordinary dierential equations using various BVCs. Boundary value problems (for short BVPs) for fourth order ordinary dierential equations (for short ODEs) are used to describe a huge number of physical, biological and chemical phenomena, see for instance [1, 11, 13, 22, 23, 27] and references therein. In the last few decades, positive solution of two-point, three-point and four-point boundary value problems for second order, third order, fourthReceived July 28, 2020, Accepted: September 27, 2020, Online: October 14, 2020.Md. Asaduzzaman, Adv. Theory Nonlinear Anal. Appl. 4 (2020), 233242
The aim of this paper is to study the more accurate existence results of positive solution for a nonlinear fourth order ordinary dierential equation using four-point boundary value conditions
It is well established that the xed point technique and upper and lower solution method are most important techniques for checking the existence of positive solutions of ordinary dierential equations using various BVCs
Summary
It is well established that the xed point technique and upper and lower solution method are most important techniques for checking the existence of positive solutions of ordinary dierential equations using various BVCs. Boundary value problems (for short BVPs) for fourth order ordinary dierential equations (for short ODEs) are used to describe a huge number of physical, biological and chemical phenomena, see for instance [1, 11, 13, 22, 23, 27] and references therein. In the last few decades, positive solution of two-point, three-point and four-point boundary value problems for second order, third order, fourthReceived July 28, 2020, Accepted: September 27, 2020, Online: October 14, 2020.Md. Asaduzzaman, Adv. Theory Nonlinear Anal. Appl. 4 (2020), 233242.
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