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The Ambrosetti–Prodi problem for elliptic systems with Trudinger–Moser nonlinearities
Published online by Cambridge University Press: 04 January 2012
Abstract
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.
MSC classification
- 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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