On a third-order boundary value problem at resonance on the half-line

Abstract

In this paper, we establish existence of solutions for the following boundary value problem on the half-line:We establish sufficient conditions for the existence of at least one solution using coincidence degree arguments. An example is provided to validate our result. Mathematics Subject Classification

On the Solvability of a Resonant Third-Order Integral m-Point Boundary Value Problem on the Half-Line

“…Theorem 4 (see [9]). Let U be the space of all bounded continuous vector-valued functions on ½0, ∞Þ and M ⊂ U.…”

“…They applied a perturbation technique in obtaining existence results under the resonant condition ∑ m−1 i=1 α i = 1. Iyase [9] used coincidence degree arguments to study existence of solutions for the multipoint boundary value problem at resonance on the half-line…”

A third-order p-laplacian boundary value problem on an unbounded domain

“…The boundary value problem (1.1) -(1.2) is then said to be at non-resonance. In [6] we proved the existence of solutions for the boundary value problem.…”

“…dt, u(0) = 0, lim t→∞ q(t)u (t) = 0 (1.4) under the resonant condition m i=1 α i ξ 2 i = 2. The method of investigation in [6] was based on coincidence degree arguments. In this work, we shall utilise topological degree methods based on the Leray-Schauder degree theory [10].…”

Higher Order Nonlocal Boundary Value Problems at Resonance on the Half-line

“…Most papers focused on boundary value problems at resonance on finite intervals especially for second and third order boundary value problems. For some results in this direction see [4,5,6,7,8,9,10,11,12,13,14,15,17,18,19] and references therein. Nonlocal boundary value problems were first studied in [3] by Bicadze and Samarskii.…”