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Superlinear elliptic problems under the non-quadraticity condition at infinity

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  30 June 2015

Marcelo F. Furtado  and
Edcarlos D. Silva
Marcelo F. Furtado
Affiliation:
Departamento de Matemática, Universidade de Brasília, 70910-900 Brasília-DF, Brazil (mfurtado@unb.br)
Edcarlos D. Silva
Affiliation:
Instituto de Matemática e Estatística, Universidade Federal de Goiás, 74001-970 Goiânia-GO, Brazil (edcarlos@mat.ufg.br)
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Abstract

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We present some sufficient conditions to obtain compactness properties for the Euler–Lagrange functional of an elliptic equation. As an application, we extend some existence and multiplicity results for superlinear problems.

Keywords

elliptic equations; superlinear problemsnon-quadraticity conditionvariational methods

MSC classification

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 4 , August 2015 , pp. 779 - 790
Copyright
Copyright © Royal Society of Edinburgh 2015