一类带有混合非线性项的基尔霍夫-薛定谔-泊松系统解的存在性

Existence of solutions to a class of Kirchhoff-Schrodinger-Poisson system with mixed nonlinearities

研究了下述基尔霍夫-薛定谔-泊松系统解的存在问题1+b∫R3[|▽u|^2+V(x)u^2]d x[-Δu+V(x)u]+λφu=K(x)|u|^q-2 u+f(x,u),x∈R^3,-Δφ=u ^2,lim|x|→∞φ(x)=0,x∈R^3,其中λ>0,b≥0,1<q<2且f(x,u)关于u在无穷远处是线性有界的.在V,K和f满足一定假设下,通过使用变分方法,得到该系统负能量非平凡解以及无穷多非平凡解的存在性.

The existence and multiplicity of solutions to a class of Kirchhoff-Schrodinger-Poisson system 1+b∫R3[|▽u|^2+V(x)u^2]d x[-Δu+V(x)u]+λφu=K(x)|u|^q-2 u+f(x,u),x∈R^3,-Δφ=u ^2,lim|x|→∞φ(x)=0,x∈R^3,is studied,whereλ>0,b≥0,1<q<2 and f(x,u)is linearly bounded in u at infinity.With the help of variational methods,the system possesses nontrivial solution is gotten at negative energy.Moreover,the existence and multiplicity of solutions under some assumptions on V,K and f is proved.