MULTIPLICITY RESULTS FOR DOUBLE EIGENVALUE PROBLEMS INVOLVING THE p-LAPLACIAN

MULTIPLICITY RESULTS FOR p-SUBLINEAR p-LAPLACIAN PROBLEMS INVOLVING INDEFINITE EIGENVALUE PROBLEMS VIA MORSE THEORY

We establish some multiplicity results for a class of p-sublinear pLaplacian problems involving indefinite eigenvalue problems using Morse theory.

THE OPTIMIZATION OF EIGENVALUE PROBLEMS INVOLVING THE p-LAPLACIAN

Given a bounded domain Ω ⊂ R and numbers p > 1, α ≥ 0, A ∈ [0, |Ω|], consider the following optimization problem: find a subset D ⊂ Ω, of measure A, for which the first eigenvalue of the operator −∆p + αχD φp with the Dirichlet boundary condition is as small as possible. We prove the existence of optimal solutions and study their qualitative properties. We also obtain the radial symmetry of opt...

STEKLOV PROBLEMS INVOLVING THE p(x)-LAPLACIAN

Under suitable assumptions on the potential of the nonlinearity, we study the existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplacian. Our approach is based on variational methods.

EIGENVALUE PROBLEMS WITH p-LAPLACIAN OPERATORS

In this article, we study eigenvalue problems with the p-Laplacian operator: −(|y′|p−2y′)′ = (p− 1)(λρ(x)− q(x))|y|p−2y on (0, πp), where p > 1 and πp ≡ 2π/(p sin(π/p)). We show that if ρ ≡ 1 and q is singlewell with transition point a = πp/2, then the second Neumann eigenvalue is greater than or equal to the first Dirichlet eigenvalue; the equality holds if and only if q is constant. The same ...

Existence and Multiplicity of Solutions for Semipositone Problems Involving p-Laplacian