摘要
In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2<q<p<2^(∗)=2N/N−2,a(x)and b(x)are functions that can change sign and satisfy some additional conditions;u∈H_(A)^(1)(R^(N))and A:R^(N)→R^(N) is a magnetic potential.Also using the Nehari method in combination with other complementary arguments,we discuss the existence of infinitely many solutions to the problem in question,varying the assumptions about the weight functions.
基金
grants from FAPESP 2017/16108-6
grants from FAPESP 2019/24901-3 and CNPq 307061/2018-3
supported by CAPES/Brazil and the paper was completed while the second author was visiting the Departament of Mathematics of UFJF whose hospitality she gratefully acknowledges.
