In this paper, we study a nonlinear Schrödinger equation with competing potentials -ε2Δν V(x)ν=W1(x)|ν|p-2ν W2(x)|ν|q-2ν, ν∈H1(RN), where ε>0, p,q∈(2,2*), p>q, , V(x), W1(x) and W2(x) are continuous bounded positive functions. Under suitable assumptions on the potentials, we consider the existence, concentration, convergence and decay estimates of the ground state solution for this equation. Furthermore, the multiplicity of semi-classical solutions is established by using Benci pseudo-index theory, and the existence of sign-changing solutions is obtained via Nehari method.
Cite this paper
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