摘要
In this article,we show the existence of infinitely many solutions for the fractional p-Laplacian equations of Schrödinger–Kirchhoff type equation M([u]_(s,p)^(p))(−Δ)_(p)^(s)u+V(x)|u|^(p−2)u=λ(Iα∗|u|^(p_(s,α)^(∗)))|u|^(p_(s,α)^(∗)−2)u+βk(x)|u|^(q−2)u,x∈R^(N),where(−Δ)s p is the fractional p-Laplacian operator,[u]s,p is the Gagliardo p-seminorm,0<s<1<q<p<N/s,α∈(0,N),M and V are continuous and positive functions,and k(x)is a non-negative function in an appropriate Lebesgue space.Combining the concentration-compactness principle in fractional Sobolev space and Kajikiya’s new version of the symmetric mountain pass lemma,we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters λ and β.
基金
Supported by National Natural Science Foundation of China(Grant No.11701178)
Natural Science Foundation program of Jiangxi Provincial(Grant No.20202BABL201011)
Natural Science Foundation of Jiangxi Educational Committee(Grant No.GJJ190337)。