Abstract
Abstract The existence of at least one solution to the second-order nonlocal boundary value problems on a half line is investigated by using Mawhin’s continuation theorem. MSC: 34B10, 34B40, 34B15.
Highlights
Boundary value problems on an infinite interval arise quite naturally in the study of radially symmetric solutions of nonlinear elliptic equations and in various applications such as an unsteady flow of gas through a semi-infinite porous media, theory of drain flows and plasma physics
For an extensive collection of results as regards boundary value problems on unbounded domains, we refer the reader to a monograph by Agarwal and O’Regan [ ]
Resonance problems can be expressed as an abstract equation Lx = Nx, where L is a noninvertible operator
Summary
Boundary value problems on an infinite interval arise quite naturally in the study of radially symmetric solutions of nonlinear elliptic equations and in various applications such as an unsteady flow of gas through a semi-infinite porous media, theory of drain flows and plasma physics. When L is linear, Mawhin’s continuation theorem [ ] is an efficient tool in finding solutions for these problems. There have been many works concerning the existence of solutions for multi-point boundary value problems at resonance. We consider the existence of solutions to the following second-order nonlinear differential equation with nonlocal boundary conditions that contain integral and multi-point boundary conditions:. The purpose of this paper is to establish the sufficient conditions for the existence of solutions to problem ( ) on a half line at resonance with dim(ker L) = by using Mawhin’s continuation theorem [ ]. Since the Arzelá-Ascoli theorem fails in the noncompact interval case, we use the following result in order to show that KP(I – Q)N : → X is compact.
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