Abstract
In this paper we are considering a third-order three-point equation with nonhomogeneous conditions in the boundary. Using Krasnoselskii's Theorem and Leray-Schauder Alternative we provide existence results of positive solutions for this problem. Nontrivials examples are given and a numerical method is introduced.
Highlights
Multi-point boundary value problems there has been attention of several studies mainly focused on the existence of solutions with qualitative and quantitative aspects, we recommend [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15] and the references therein
In this paper, motived by [13], we discuss the existence of a positive solution for the third-order boundary value problem: u + f (t, u, u ) = 0, 0 < t < 1, (1.1)
2 BACKGROUND MATERIAL We begin this section by stating the following results
Summary
Multi-point boundary value problems there has been attention of several studies mainly focused on the existence of solutions with qualitative and quantitative aspects, we recommend [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15] and the references therein. In this paper, motived by [13], we discuss the existence of a positive solution for the third-order boundary value problem:. We combine Leray-Schauder Alternative and Krasnoselskii’s theorem to show the existence of a positive solution for (1.1)-(1.2) without supposing superlinearity on f. 418 THIRD-ORDER THREE-POINT NONHOMOGENEOUS BOUNDARY VALUE PROBLEM explored, we complement this work presenting a numerical study for (1.1)-(1.2) based on Banach’s Contraction Principle
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