N-Laplacian equations in ℝN with critical growthReport as inadecuate




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Abstract and Applied Analysis - Volume 2 1997, Issue 3-4, Pages 301-315

Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa 58059.900, Pb, Brazil

Received 10 June 1997

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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





Author: João Marcos B. do Ó

Source: https://www.hindawi.com/



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