科研之友
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摘要
We consider the following singularly perturbed Kirchhoff-type equations ? ? ? -epsilon 2M epsilon 2-N RN |Vu|2dx ?u + V(x)u = |u|p-2u in RN, u E H1(RN), N >_ 1, where M E C([0, oo)) and V E C(RN) are given functions. Under very mild assumptions on M, we prove the existence of single-peak or multi-peak solution u epsilon for above problem, concentrating around topologically stable critical points of V, by a direct corresponding argument. This gives an affirmative answer to an open problem raised by Figueiredo et al. (Arch Ration Mech Anal 213(3):931-979, 2014)
