Abstract
IntroductionNeumann boundary value problems have been studied by many authors. We are mainly interested in the semi-positone case. This paper deals with the existence and multiplicity of positive solutions of a superlinear semi-positone singular Neumann boundary value problem.PreliminariesThe proof of our main results relies on a nonlinear alternative of Leray-Schauder type, the method of upper and lower solutions and on a well-known fixed point theorem in cones.Main resultsWe obtained the existence of at least two different positive solutions.
Highlights
Neumann boundary value problems have been studied by many authors
1 Introduction We will be concerned with the existence and multiplicity of positive solutions of the superlinear singular Neumann boundary value problem in the semi-positone case
By the semi-positone case of ( . ), we mean that g(x, u) may change sign and satisfies F(x, u) = g(x, u) + M ≥ where M > is a constant
Summary
It is well known that the existence of positive solutions of boundary value problems has been studied by many authors in [ – ] and references therein. They mainly considered the case of p(x) ≡ and q(x) ≡. In [ ], the authors studied positive solutions of Neumann boundary problems of second order impulsive differential equations in the positone case, based on a nonlinear alternative principle of Leray-Schauder type and a well-known fixed point theorem in cones. This paper attempts to study the existence and multiplicity of positive solutions of second order superlinear singular Neumann boundary value problems in the semi-positone case. In Section , we state and prove the main results of this paper
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