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ambrosetti–prodi problem

Proceedings of the Edinburgh Mathematical Society (1)

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The Ambrosetti–Prodi problem for elliptic systems with Trudinger–Moser nonlinearities
Part of
- Elliptic equations and systems
Bruno Ribeiro
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 1 / February 2012

Published online by Cambridge University Press:

04 January 2012, pp. 215-244
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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.