The existence and concentration of positive ground state solutions for a class of fractional Schrödinger-Poisson systems with steep potential wells

Abstract

The present study is concerned with the following fractional Schrödinger-Poisson system with steep potential well: $$ \left\{% \begin{array}{ll} (-Δ)^s u+ \la V(x)u+K(x)ϕu= f(u), & x\in\R^3, (-Δ)^t ϕ=K(x)u^2, & x\in\R^3, \end{array}% \right. $$ where $s,t\in (0,1)$ with $4s+2t>3$, and $\la>0$ is a parameter. Under certain assumptions on $V(x)$, $K(x)$ and $f(u)$ behaving like $|u{|}^{q-2}u$ with $2<q<2_s^{\ast }=\frac{6}{3-2s}$, the existence of positive ground state solutions and concentration results are obtained via some new analytical skills and Nehair-Pohožaev identity. In particular, the monotonicity assumption on the nonlinearity is not necessary.

21 pages

References in corpus (1)

• The existence of positive least energy solutions for a class of Schrodinger-Poisson systems involving critical nonlocal term with general nonlinearity