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Solutions to a perturbed critical semilinear equation concerning the N -Laplacian in N

Elliot Tonkes — 1999

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to study the existence of variational solutions to a nonhomogeneous elliptic equation involving the N -Laplacian - Δ N u - div ( | u | N - 2 u ) = e ( x , u ) + h ( x ) in Ω where u W 0 1 , N ( N ) , Ω is a bounded smooth domain in N , N 2 , e ( x , u ) is a critical nonlinearity in the sense of the Trudinger-Moser inequality and h ( x ) ( W 0 1 , N ) * is a small perturbation.

Symmetric integrals and trigonometric series

CONTENTS 1. Introduction............................................................................................5 2. Some preliminary definitions..................................................................6 3. Mařík's symmetric difference..................................................................9 4. Basic definitions...................................................................................11 5. Properties of the second symmetric variation for real functions...........15 6....

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