On the existence of multipeak solutions for nonlinear field equations on $R^N$

E. N. Dancer; Shusen Yan

doi:10.3934/dcds.2000.6.39

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2000, Volume 6, Issue 1: 39-50. Doi: 10.3934/dcds.2000.6.39

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On the existence of multipeak solutions for nonlinear field equations on $R^N$

E. N. Dancer^1, and
Shusen Yan^2,

1.
School of Mathematics and Statistics, University of Sydney, N.S.W. 2006
2.
School of Mathematics and Statistics, University of Sydney, NSW 2006

Received: September 1999

Published: January 2000

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we construct multipeak solutions with all the peaks close to a designated saddle point or strict local minimum point of the function $Q(y)$ for the nonlinear field equations. We also show that there is no multipeak solution with all its peaks near a strict local maximum point of $Q(y)$.

Keywords:

elliptic problem,
multipeak solution.

Mathematics Subject Classification: 35B25, 35J65.

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