Abstract
Existence of solution for a nonlinear fifth-order three-point boundary value problem
Highlights
The study of fourth-order three-point boundary value problems (BVP) for ordinary differential equations arise in a variety of different areas of applied mathematics and physics
In this paper, we explore the existence of nontrivial solution for the fifth-order three-point boundary value problem of the form u(5)(t) + f (t, u(t)) = 0, 0 < t < 1, with boundary conditions u(0) = 0, u (0) = u (0) = u (0) = 0, u(1) = αu(η), where 0 < η < 1, α ∈ R, αη4 = 1, f ∈ C([0, 1] × R, R)
Various authors studied the existence of positive solutions for nth-order m-point boundary value problems using different methods, for example, fixed point theorems in cones, nonlinear alternative of Leray-Schauder, and Krasnoselskii’s fixed point theorem, see [1–5] and the references therein
Summary
The study of fourth-order three-point boundary value problems (BVP) for ordinary differential equations arise in a variety of different areas of applied mathematics and physics. Abstract: In this paper, we explore the existence of nontrivial solution for the fifth-order three-point boundary value problem of the form u(5)(t) + f (t, u(t)) = 0, 0 < t < 1, with boundary conditions u(0) = 0, u (0) = u (0) = u (0) = 0, u(1) = αu(η), where 0 < η < 1, α ∈ R, αη4 = 1, f ∈ C([0, 1] × R, R).
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