On some nonlinear Neumann problem with weight and critical Sobolev trace maps - Archive ouverte HAL Access content directly
Journal Articles Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Year : 2007

On some nonlinear Neumann problem with weight and critical Sobolev trace maps

Abstract

We consider the problem - div(p(x)del u) = lambda u + alpha vertical bar u vertical bar(r-1)u in Q, partial derivative u/partial derivative nu = Q(x)vertical bar u(q-2)u on partial derivative ohm, where ohm is a bounded smooth domain in R-N, N >= 3, q = 2(N - 1)/(N - 2) and 2 < r < q. Under some conditions on partial derivative ohm, p, Q, lambda, alpha and the mean curvature at some point x(0), we prove the existence of solutions of the above problem. We use variational arguments, namely the concentration-compactness principle, min-max principle and the mountain-pass theorem.
No file

Dates and versions

hal-00693096 , version 1 (01-05-2012)

Identifiers

  • HAL Id : hal-00693096 , version 1

Cite

Habib Yazidi. On some nonlinear Neumann problem with weight and critical Sobolev trace maps. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2007, 137 (?), pp.647--670. ⟨hal-00693096⟩
35 View
0 Download

Share

Gmail Facebook Twitter LinkedIn More