摘要
In this paper,we consider the following Schrodinger-Poisson system{-ε^(2)Δu+V(x)u+K(x)Φ(x)u=|u|^(p-1)u in R^(N),-ΔΦ(x)=K(x)u^(2)in RN,,where e is a small parameter,1<p<N+2/N-2,N∈[3,6],and V(x)and K(x)are potential functions with different decay at infinity.We first prove the non-degeneracy of a radial low-energy solution.Moreover,by using the non-degenerate solution,we construct a new type of infinitely many solutions for the above system,which are called“dichotomous solutions”,i.e.,these solutions concentrate both in a bounded domain and near infinity.
基金
supported by National Natural Science Foundation of China(Grant Nos.12101274 and 12226309)
the Jiangxi Province Science Fund for Distinguished Young Scholars(Grant No.20224ACB218001)
supported by National Natural Science Foundation of China(Grant No.12271223)
Jiangxi Provincial Natural Science Foundation(Grant No.20212ACB201003)
Jiangxi Two Thousand Talents Program(Grant No.jxsq2019101001)
Double-high Talents Program in Jiangxi Province。