Existence of an unbounded branch of the set of solutions for Neumann problems involving the
1 Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea
2 Department of Mathematics Education, Sangmyung University, Seoul, 110-743, Republic of Korea
Boundary Value Problems 2014, 2014:92 doi:10.1186/1687-2770-2014-92Published: 6 May 2014
We are concerned with the following nonlinear problem: in Ω, on ∂Ω, which is subject to a Neumann boundary condition, provided that μ is not an eigenvalue of the -Laplacian. The aim of this paper is to study the structure of the set of solutions for the degenerate -Laplacian Neumann problems by applying a bifurcation result for nonlinear operator equations.
MSC: 35B32, 35D30, 35J70, 47J10, 47J15.