摘要
主要通过变分法得到一类在无穷远处具有Fucik谱共振的Kirchhoff型方程{-(∫Ω|▽u|^(2)dx)Δu=α(u+)^(3)+β(u-)^(3)+f(x,u)x∈Ωu=0x∈∂Ω非平凡解的存在性.其中Ω是RN(N=1,2,3)中的开球,α,β∈R,u+=max{u,0},u-=min{u,0},u=u++u-.非线性项f∈C(Ω×R,R)满足f(x,0)=0.应用带有(Ce)条件的山路定理,得到该方程在Fucik谱的两条平凡曲线上非平凡解的存在性.
In this paper,we obtain the existence of non-trivial solutions for the Kirchhoff type equation with Fucik-type resonance at infinity by variational methods.{-∫Ω|▽u|^(2)dxΔu=α(u+)^(3)+β(u-)^(3)+f(x,u)x∈Ωu=0x∈∂ΩwhereΩis an open ball in RN(N=1,2,3),α,β∈R,u+=max{u,0},u-=min{u,0},and u=u++u-.The nonlinear term f∈C(Ω×R,R)satisfies f(x,0)=0.By using Mountain Pass Theorem with(Ce)condition,we obtain the existence of nontrivial solutions for the equations on two trivial curves of Fucik spectrum.
作者
陈兴菊
欧增奇
CHEN Xing-ju;OU Zeng-qi(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)
出处
《西南师范大学学报（自然科学版）》
CAS
2021年第8期24-31,共8页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(11801465,11971393).
