一类变指数基尔霍夫型方程的无穷多解  

Infinitely Many Solutions for a Class of Kirchhoff-type Equation with Variable Exponent

作　　者：张申贵[1] ZHANG SHENGUI(School of Mathematics and Computer Science,Northwest Minzu University,Lanzhou,730030)

机构地区：[1]西北民族大学数学与计算机科学学院

出　　处：《应用数学学报》2018年第6期801-810,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(31260098);中央高校基本科研业务费专项基金(31920180041)资助项目

摘　　要：本文研究带有各向异性p(x)-Laplace算子的基尔霍夫型方程Dirichlet边值问题-N∑i=1Mi(∫Ω|xiu|pi(x)pi(x)dxxi(|xiu|(pi(x)-2xiu=H(∫ΩF(x,u)dx)f(x,u),x∈Ω,u=0,x∈Ω其中Ω是RN(N≥3)中具有光滑边界的有界区域,f(x,u)∈C(×R,R),,i=1,2,…,N,且Mi(t):R+→R+,H(t):R→R和pi(x):→R为连续函数.当非线性项在零点附近次线性增长时,运用临界点理论中的Clark定理获得了新的多重解存在性结果.In this paper, we investigate the following Dirichlet boundary value problem for Kirchhoff-type equation involving the anisotropic p(x)-Laplacian operator-N∑i=1Mi(∫Ω|xiu|pi(x)pi(x)dxxi(|xiu|(pi(x)-2xiu=H(∫ΩF(x,u)dx)f(x,u),x∈Ω,u=0,x∈Ωwhere ΩRN(N≥3)is a bounded domain with smooth boundary, f(x,u) ∈ C(×R,R),, i=1,2,…,N, Mi(t) : R+→R+, H(t) : R→R and Pi(x):→R are continuous functions. When the nonlinearity has a sublinear growth near zero, some new results for existence of multiplicity of solutions are obtained by using the Clark’s theorem in critical point theory.

关 键 词：基尔霍夫型方程 DIRICHLET边值问题 各向异性p(x)-Laplace算子 临界点理论 

分 类 号：O177.91[理学—数学] O175.25[理学—基础数学]