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On a Class of Semilinear Elliptic Eigenvalue Problems in ℝ2

Published online by Cambridge University Press:  19 May 2016

Marcelo F. Furtado
Affiliation:
Universidade de Brasília, Departamento de Matemática, 70910-900 Brasília-DF, Brazil ([email protected])
Everaldo S. Medeiros
Affiliation:
Universidade Federal do Paraíba, Departamento de Matemática, 58051-900 João Pessoa-PB, Brazil ([email protected]; [email protected])
Uberlandio B. Severo
Affiliation:
Universidade Federal do Paraíba, Departamento de Matemática, 58051-900 João Pessoa-PB, Brazil ([email protected]; [email protected])

Abstract

We consider the semilinear problem

where λ is a positive parameter and f has exponential critical growth. We first establish the existence of a non-zero weak solution. Then, by assuming that f is odd, we prove that the number of solutions increases when the parameter λ becomes large. In the proofs we apply variational methods in a suitable weighted Sobolev space consisting of functions with rapid decay at infinity.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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