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Multiplicity of positive solutions for a class of problems with critical growth in ℝN

Published online by Cambridge University Press:  02 February 2009

Claudianor O. Alves
Affiliation:
Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística, CEP 58109-970, Campina Grande-PB, Brazil ([email protected])
Daniel C. de Morais Filho
Affiliation:
Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística, CEP 58109-970, Campina Grande-PB, Brazil ([email protected])
Marco A. S. Souto
Affiliation:
Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística, CEP 58109-970, Campina Grande-PB, Brazil ([email protected])
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Abstract

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Using variational methods, we establish the existence and multiplicity of positive solutions for the following class of problems:

where λ,β∈(0,∞), q∈(1,2*−1), 2*=2N/(N−2), N≥3, V,Z:ℝN→ℝ are continuous functions verifying some hypotheses.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2009