N-Laplacian equations in ℝN with critical growth

N-Laplacian equations in ℝN with critical growth

We study the existence of nontrivial solutions to the following problem: {u∈W1,N(ℝN),u≥0  and−div(|∇u|N−2∇u)+a(x)|u|N−2u=f(x,u)  in  ℝN(N≥2), where a is a continuous function which is coercive, i.e., a(x)→∞ as |x|→∞ and the nonlinearity f behaves like exp(α|u|N/(N−1)) when |u|→∞....

Full description

Bibliographic Details
Main Author: João Marcos B. do Ó
Format: Article
Language:English
Published: Hindawi Limited 1997-01-01
Series:Abstract and Applied Analysis
Subjects:
Elliptic equations
p-Laplacian
critical growth
Mountain Pass theorem
Trudinger-Moser inequality.
Online Access:http://dx.doi.org/10.1155/S1085337597000419
id doaj-351f2a45fe2b427397f297dac20d09f9
record_format Article
spelling doaj-351f2a45fe2b427397f297dac20d09f92020-11-24T23:01:54ZengHindawi LimitedAbstract and Applied Analysis1085-33751997-01-0123-430131510.1155/S1085337597000419N-Laplacian equations in ℝN with critical growthJoão Marcos B. do Ó0Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa 58059.900, Pb, BrazilWe study the existence of nontrivial solutions to the following problem: {u∈W1,N(ℝN),u≥0  and−div(|∇u|N−2∇u)+a(x)|u|N−2u=f(x,u)  in  ℝN(N≥2), where a is a continuous function which is coercive, i.e., a(x)→∞ as |x|→∞ and the nonlinearity f behaves like exp(α|u|N/(N−1)) when |u|→∞.http://dx.doi.org/10.1155/S1085337597000419Elliptic equationsp-Laplaciancritical growthMountain Pass theoremTrudinger-Moser inequality.
collection DOAJ
language English
format Article
sources DOAJ
author João Marcos B. do Ó
spellingShingle João Marcos B. do Ó
N-Laplacian equations in ℝN with critical growth
Abstract and Applied Analysis
Elliptic equations
p-Laplacian
critical growth
Mountain Pass theorem
Trudinger-Moser inequality.
author_facet João Marcos B. do Ó
author_sort João Marcos B. do Ó
title N-Laplacian equations in ℝN with critical growth
title_short N-Laplacian equations in ℝN with critical growth
title_full N-Laplacian equations in ℝN with critical growth
title_fullStr N-Laplacian equations in ℝN with critical growth
title_full_unstemmed N-Laplacian equations in ℝN with critical growth
title_sort n-laplacian equations in ℝn with critical growth
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
publishDate 1997-01-01
description We study the existence of nontrivial solutions to the following problem: {u∈W1,N(ℝN),u≥0  and−div(|∇u|N−2∇u)+a(x)|u|N−2u=f(x,u)  in  ℝN(N≥2), where a is a continuous function which is coercive, i.e., a(x)→∞ as |x|→∞ and the nonlinearity f behaves like exp(α|u|N/(N−1)) when |u|→∞.
topic Elliptic equations
p-Laplacian
critical growth
Mountain Pass theorem
Trudinger-Moser inequality.
url http://dx.doi.org/10.1155/S1085337597000419
work_keys_str_mv AT joaomarcosbdoo nlaplacianequationsinrnwithcriticalgrowth
_version_ 1725638363380187136

Similar Items