A Kirchhoff-type problem involving concave-convex nonlinearities

Advances in Difference Equations

Yonghong Wu¹  Lishan Liu²  Yuan Gao²  Shixia Luan² 

[1] Department of Mathematics and Statistics, Curtin University, 6845, Perth, WA, Australia;School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, Shandong, People’s Republic of China;

关键词: Concave-convex nonlinearities;    Kirchhoff-type problem;    Nehari manifolds;    Ground state sign-changing solutions;    35J20;    35J65;    35A15;    35J60;   

DOI  :  10.1186/s13662-021-03331-x

来源: Springer

【 摘 要 】

A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy. Moreover, we show that the energy level of this sign-changing solution is strictly larger than the double energy level of the ground state solution.

【 授权许可】

CC BY