Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024363 | Nonlinear Analysis: Real World Applications | 2018 | 26 Pages |
Abstract
In this paper, we study the following Hamiltonian elliptic system with gradient term âϵ2ÎÏ+ϵbââ
âÏ+Ï+V(x)Ï=âi=1IKi(x)|η|piâ2ÏinRN,âϵ2ÎÏâϵbââ
âÏ+Ï+V(x)Ï=âi=1IKi(x)|η|piâ2ÏinRN,where η=(Ï,Ï):RNâR2, V,KiâC(RN,R), ϵ>0 is a small parameter and bâ is a constant vector. Suppose that V is sign-changing and has at least one global minimum, and Ki has at least one global maximum. We prove that there are two families of semiclassical solutions, for sufficiently small ϵ, with the least energy, one concentrating on the set of minimal points of V and the other on the set of maximal points of Ki. Moreover, the convergence and exponential decay of semiclassical solutions are also explored.
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Authors
Jian Zhang, Wen Zhang, Xianhua Tang,