A Weighted Eigenvalue Problems Driven by both p(·)-Harmonic and p(·)-Biharmonic Operators

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 ...

A Note on Weighted Composition Operators on L^p-Spaces

Existence 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)] .

Existence of at least one nontrivial solution for a class of problems involving both p(x)-Laplacian and p(x)-Biharmonic

We investigate the existence of a weak nontrivial solution for the following problem. Our analysis is generally bathed on discussions of variational based on the Mountain Pass theorem and some recent theories one the generalized Lebesgue-Sobolev space. This paper guarantees the existence of at least one weak nontrivial solution for our problem. More precisely, by applying Ambrosetti and Rabinow...

a note on weighted composition operators on l^p-spaces