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: https://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

Published 1 January 2008