一类非线性Schrdinger-Kirchhoff系统非平凡解的存在性

Existence of Nontrivial Solution for a Class of the Nonlinear Schrdinger-Kirchhoff System with Potential

文章主要讨论带有位势V(x)的非线性Schrdinger-Kirchhoff型方程﹛(a+b∫[|▽u|~2+V(x)u^2])[-Δu+V(x)u]+λh(x)φu=g(x,u),x∈R3,-Δφ=λh(x)u^2,x∈R^3.(1)(λ≥0)非平凡解的存在性,利用山路定理得到其至少存在一个非平凡解.

We study the existence of nontrivial solution for the nonlinear Sehr6dinger- Kirchhoff system with potential.{（a＋b∫[△u丨2＋V（x）u2^][-△u＋V（x）u]＋λh（x）φu=g（x,y）,x∈R3,-△φ=λh（x）u2^,x∈R3^.（λ≥0） By using Mountain pass theorem in variational method, we prove that there exist at least one nontrivial solution.