局部有限图上非线性方程解的存在性  

Existence of Positive Solutions to Nonlinear Equations on Locally Finite Graphs

作　　者：吴璐 KHINE Minminoo WU Lu(College of Mathematics,Physics and Information Engineering,zhejiang Normal University,Jinhua Zhejiang 321004,China)

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《上饶师范学院学报》2018年第6期5-9,共5页Journal of Shangrao Normal University

基　　金：国家自然科学基金资助项目(11571317)

摘　　要：在局部有限图G=(V,E)上考虑方程:-Δu+h(x)u=f(x,u), x∈V(P)解的存在性。其中f:V×R→R,f(x,t)/t关于t单调不减,并且f(x,t)关于t在无穷远处是渐近线性的。在没有(AR)条件的情况下,应用山路引理证明了方程(P)解的存在性。We consider the existence of solution for equation:-Δu+h(x)u=f(x,u),x∈V(P)on locally finite graphs G=(V,E).Where f:V×R→R,f(x,t)/t is nondecreasing in t∈R and f(x,t)is asymptotically linear in t at infinity.In this paper,without assuming(AR)we prove,by using mountain pass theorem,that equation(P)has a solution.

关 键 词：山路引理 变分法 渐进线性 图上的半线性方程 

分 类 号：O175.25[理学—数学]