Abstract
Abstract By using the bifurcation method, we study the existence of an S-shaped connected component in the set of positive solutions for discrete second-order Neumann boundary value problem. By figuring the shape of unbounded connected component of positive solutions, we show that the Neumann boundary value problem has three positive solutions suggesting suitable conditions on the weight function and nonlinearity.
Highlights
We are concerned with the existence and multiplicity of positive solutions for the following second-order Neumann boundary value problem
Second-order Neumann boundary value problems have attracted the attention of many specialists both in differential equations and difference equations because of their interesting applications, see [1,2,3,4,5,6,7,8,9,10] and references therein
In high-dimensional case, several results of existence and multiplicity can be found for Neumann boundary value problems associated with
Summary
We are concerned with the existence and multiplicity of positive solutions for the following second-order Neumann boundary value problem S-shaped connected component of positive solutions 1659 solutions of problem (1.2). Boscaggin [3], Boscaggin and Zanolin [4] and Boscaggin and Garrione [6] studied the existence and multiplicity of positive solutions for problem (1.2). In high-dimensional case, several results of existence and multiplicity can be found for Neumann boundary value problems associated with
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