MULTIPLE SOLUTIONS FOR A DIRICHLET PROBLEM WITH p-LAPLACIAN AND SET-VALUED NONLINEARITY
نویسندگان
چکیده
The existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via suband supersolution methods as well as variational techniques for nonsmooth functions. 2000 Mathematics subject classification: 35J20, 35J85, 49J40.
منابع مشابه
A VARIATIONAL APPROACH TO THE EXISTENCE OF INFINITELY MANY SOLUTIONS FOR DIFFERENCE EQUATIONS
The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...
متن کاملExistence Results For Dirichlet Problems With Degenerated p-Laplacian And p-Biharmonic Operators∗
In this article, we prove the existence and uniqueness of solutions for the Dirichlet problem (P ) { ∆(ω(x)|∆u|∆u)− div[ω(x)|∇u|∇u] = f(x)− div(G(x)), in Ω u(x) = 0, in ∂Ω where Ω is a bounded open set of R (N≥2), f∈L (Ω, ω) and G/ω∈[L (Ω, ω)] .
متن کاملBIFURCATION ALONG CURVES FOR THE p-LAPLACIAN WITH RADIAL SYMMETRY
We study the global structure of the set of radial solutions of a nonlinear Dirichlet eigenvalue problem involving the p-Laplacian with p > 2, in the unit ball of RN , N > 1. We show that all non-trivial radial solutions lie on smooth curves of respectively positive and negative solutions, bifurcating from the first eigenvalue of a weighted p-linear problem. Our approach involves a local bifurc...
متن کاملGraphs of Finite Measure
We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of ‘relative compactness’ for such graphs and study sufficient and necessary conditions for this property in terms of various metrics. We then equip graphs satisfying this property with a finite measure and investigate the associated Laplacian and its ...
متن کاملConvergence Analysis of a Galerkin Boundary Element Method for the Dirichlet Laplacian Eigenvalue Problem
In this paper, a rigorous convergence and error analysis of a Galerkin boundary element method for the Dirichlet Laplacian eigenvalue problem is presented. The formulation of the eigenvalue problem in terms of a boundary integral equation yields a nonlinear boundary integral operator eigenvalue problem. This nonlinear eigenvalue problem and its Galerkin approximation are analyzed in the framewo...
متن کامل