Quasilinear elliptic equations with critical exponents

Quasilinear Elliptic Equations with Critical Exponents

has no solution if Ω ⊂ R , N ≥ 3, is bounded and starshaped with respect to some point, and 2∗ = 2N/(N − 2). In (P0) the nonlinear term is a power of u with the critical exponent (N + 2)/(N − 2). This terminology comes from the fact that the continuous Sobolev imbeddings H 0 (Ω) ⊂ L(Ω), for p ≤ 2∗ and Ω bounded, are also compact except when p = 2∗. This loss of compactness reflects in that the ...

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

Quasilinear Elliptic Problems with Critical Exponents and Discontinuous Nonlinearities

Using a recent fixed point theorem in ordered Banach spaces by S. Carl and S. Heikkilä, we study the existence of weak solutions to nonlinear elliptic problems −diva(x,∇u) = f (x,u) in a bounded domain Ω ⊂ Rn with Dirichlet boundary condition. In particular, we prove that for some suitable function g , which may be discontinuous, and δ small enough, the p -Laplace equation −div(|∇u|p−2∇u) = |u|...

Quasilinear Schrödinger equations involving critical exponents in $mathbb{textbf{R}}^2$

‎We study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth‎. ‎This model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

Critical Exponents and Dimensions for Elliptic Equations