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1996 Semilinear Dirichlet problems for the $N$-Laplacian in $\mathbb{R}^N$ with nonlinearities in the critical growth range
João Marcos B. do Ó
Differential Integral Equations 9(5): 967-979 (1996).

Abstract

The goal of this paper is to study the existence of solutions for the following class of problems for the $N$-Laplacian $$ u\in W_0^{1,N}(\Omega),\quad u\geq 0\ \ \text{ and } \ \ -\Delta_Nu\equiv -\text{div}( | \nabla u | ^{N-2}\nabla u)=f(x,u) \,\,\, \rm{in}\,\,\, \Omega , $$ where $\Omega $ is a bounded smooth domain in $\Bbb R^N$ with $N\geq 2$ and the nonlinearity $f(x,u)$ behaves like $\exp (\alpha | u | ^{\frac N{N-1}})$ when $ | u | \to \infty .$

Citation

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João Marcos B. do Ó. "Semilinear Dirichlet problems for the $N$-Laplacian in $\mathbb{R}^N$ with nonlinearities in the critical growth range." Differential Integral Equations 9 (5) 967 - 979, 1996.

Information

Published: 1996
First available in Project Euclid: 6 May 2013

zbMATH: 0858.35043
MathSciNet: MR1392090

Subjects:
Primary: 35J65

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.9 • No. 5 • 1996
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