Singular perturbed problems in the zero mass case: asymptotic behavior of spikes

Singular perturbed problems in the zero mass case: asymptotic behavior of spikes

E. N. Dancer;Sanjiban Santra;E. N. Dancer;Sanjiban Santra;
annali di matematica pura ed applicata 2009 Vol. 189 pp. 185-225
174
dancer2009annalisingular

Abstract

We discuss the asymptotic behavior of the least energy solution of a Dirichlet problem in the zero mass case. If Q is a uniformly positive potential having k isolated local minima, then we prove the existence of a positive multi-spike solutions having k peaks concentrating at each local minima of the potential.

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