S-shaped connected component of positive solutions for second-order discrete Neumann boundary value problems

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.

Keywords

• three positive solutions
• discrete
• neumann boundary value problem
• bifurcation
• 39a28
• 39a21
• 39a12