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January  2000, 6(1): 39-50. doi: 10.3934/dcds.2000.6.39

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, Australia
2. 

School of Mathematics and Statistics, University of Sydney, NSW 2006

Received  September 1999 Published  December 1999

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: multipeak solution., elliptic problem.
Mathematics Subject Classification: 35B25, 35J6.
Citation: E. N. Dancer, Shusen Yan. On the existence of multipeak solutions for nonlinear field equations on $R^N$. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 39-50. doi: 10.3934/dcds.2000.6.39
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