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 applicata2009Vol. 189pp. 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.