Quasilinear elliptic equations on convex domains

Regularity and nonexistence results for anisotropic quasilinear elliptic equations in convex domains

For a class of anisotropic elliptic problems in bounded domains Ω we show that the convexity of Ω plays an important role in regularity and nonexistence results. Using recent results in [9] we improve some statements in [3]. 2000 Mathematical Subject Classification: 35J70, 46E35, 35B65.

On Quasilinear Elliptic Equations in Ir

In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −∆u = h(x)u in IR , where 0 < q < 1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.

On global bifurcation for quasilinear elliptic systems on bounded domains

Article history: Received 30 May 2008 Revised 10 September 2008 Available online 16 October 2008 MSC: primary 35J55, 35B32 secondary 46T20, 58C25, 92D25

Large Solutions for Quasilinear Elliptic Equations

Anisotropic quasilinear elliptic equations with variable exponent

We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory. 2000 Mathematics Subject Classification: 35J60, 35J62, 35J70.