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The Ambrosetti–Prodi problem for elliptic systems with Trudinger–Moser nonlinearities

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  04 January 2012

Bruno Ribeiro
Bruno Ribeiro
Affiliation:
Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa PB, Brazil ([email protected])
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Abstract

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In this work we study the following class of elliptic systems:

where Ω ⊂ ℝ2 is a smooth bounded domain, H is a C1 function in [0, +∞)×[0, +∞) which is assumed to be in the critical growth range of Trudinger–Moser type and f1, f2 ∈ Lr (Ω), r > 2. Under suitable hypotheses on the functions a, b, c ∈ C( and using variational methods, we prove the existence of two solutions depending on f1 and f2.

Keywords

systems of elliptic equationsAmbrosetti–Prodi problemTrudinger–Moser inequality

MSC classification

Secondary: 35J50: Variational methods for elliptic systems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 215 - 244
Copyright
Copyright © Edinburgh Mathematical Society 2011

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