Infinitely many bound state solutions of Kirchhoff problem in R3. (June 2016) - Xie, Qilin; Ma, Shiwang; Zhang, Xu
Abstract: In the present paper, we consider the following Kirchhoff problem ( K ) { − ( 1 + b ∫ R 3 | ∇ u | 2 d x ) Δ u + a ( x ) u = | u | p − 2 u, in R 3, u ∈ H 1 ( R 3 ), where b > 0 and p ∈ ( 4, 6 ) . Under some suitable decay assumptions but without any symmetry property on a ( x ), we obtain infinitely many bound state solutions of this problem.