Multiplicity Results for the px-Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition

[摘要] We investigate the singular Neumann problem involving the p(x)-Laplace operator: P?{-?pxu+|u|px-2u??=1/u?x+fx,u, in ??;??u>0,??in???;???upx-2?u/??=?uqx,??on????}, where ??RNN?2 is a bounded domain with C2 boundary, ? is a positive parameter, and px,qx,?x, and fx,u are assumed to satisfy assumptions (H0)–(H5) in the Introduction. Using some variational techniques, we show the existence of a number ??0,? such that problem P? has two solutions for ??0,?, one solution for ?=?, and no solutions for ?>?.

[学科分类] 几何与拓扑