Methods and Applications of Analysis

Volume 15 (2008)

Number 1

On the Lazer-McKenna Conjecture Involving Critical and Super-critical Exponents

Pages: 97 – 120

DOI: http://dx.doi.org/10.4310/MAA.2008.v15.n1.a9

Authors

E. N. Dancer

Shusen Yan

Abstract

We prove the Lazer-McKenna conjecture for an elliptic problem of Ambrosetti-Prodi type with critical and supercritical nonlinearities by constructing solutions concentrating on higher dimensional manifolds, under some partially symmetric assumption on the domain.

Keywords

Elliptic equation; multiplicity; reduction method

2010 Mathematics Subject Classification

35J65

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