On a p-Laplace equation with multiple critical nonlinearities
نویسندگان
چکیده
منابع مشابه
MULTIPLE SOLUTIONS OF A p(x)-LAPLACIAN EQUATION INVOLVING CRITICAL NONLINEARITIES
In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions { −div(|∇u|p(x)−2 ∇u) + |u|p(x)−2 u = f(x, u) in Ω, u = 0 on ∂Ω. We show the existence of infinitely many pairs of solutions by applying the Fountain Theorem and the Dual Fountain Theorem respectively. We also present a variant of the concentration-co...
متن کاملMULTIPLE SOLUTIONS FOR THE p−LAPLACE OPERATOR WITH CRITICAL GROWTH
In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation −∆pu = |u| ∗ u + λf(x, u) in a smooth bounded domain Ω of R with homogeneous Dirichlet boundary conditions on ∂Ω, where p = Np/(N − p) is the critical Sobolev exponent and ∆pu = div(|∇u|∇u) is the p−laplacian. The proof is based on variational arguments and the classical con...
متن کاملFibered nonlinearities for p(x)-Laplace equations
The purpose of this paper is to give some geometric results on the following problem: −div ( α(x)|∇u(X)|p(x)−2∇u(X) ) = f(x, u(X)) in Ω, (1.1) where f = f(x, u) ∈ L∞(Rm×R) is differentiable in u with fu ∈ L∞(R), α ∈ L∞(Rm), with inf Rm α > 0, p ∈ L∞(Rm), with p(x) ≥ 2 for any x ∈ R, and Ω is an open subset of R. Here, u = u(X), with X = (x, y) ∈ R × Rn−m. As well known, the operator in (1.1) co...
متن کاملExistence of a positive solution for a p-Laplacian equation with singular nonlinearities
In this paper, we study a class of boundary value problem involving the p-Laplacian oprator and singular nonlinearities. We analyze the existence a critical parameter $lambda^{ast}$ such that the problem has least one solution for $lambdain(0,lambda^{ast})$ and no solution for $lambda>lambda^{ast}.$ We find lower bounds of critical parameter $lambda^{ast}$. We use the method ...
متن کاملENCLOSURE METHOD FOR THE p-LAPLACE EQUATION
We study the enclosure method for the p-Calderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, wh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2009
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2008.09.008