一类具梯度项的分数阶椭圆方程解的存在性  

Existence of Solutions for a Class of Gradient Fractional Elliptic Equation

作　　者：潘柔 陈林 PAN Rou;CHEN Lin(School of Mathematics and Statistics,Yili Normal University,Yining 835000,China;Institute of Applied Mathematics,Yili Normal University,Yining 835000,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《长春师范大学学报》2024年第2期7-12,共6页Journal of Changchun Normal University

基　　金：新疆维吾尔自治区自然科学基金资助项目“基于变分法的几类椭圆方程解的存在性研究”(2022D01C459)。

摘　　要：运用山路定理与迭代的技巧证明下面分数阶椭圆方程:{(-Δ)_(p)^(s)u+V(x)u^(p-2)u=f(u,|▽u|^(p-2)▽u),u∈X^(s)(R^(N)),u(x)>0,x∈R^(N).正解的存在性,其中1<p<N,N≥2,0<s<1,(-Δ)_(p)^(s)是分数阶p-拉普拉斯算子,非线性项f:R×R^(N)→R是依赖于解的梯度项的连续函数,V(x)是正的连续函数.By using the mountain pass theorem and iterative methods to prove that the existence of positive solutions to the following fractional elliptic equation:{(-Δ)_(p)^(s)u+V(x)u^(p-2)u=f(u,|▽u|^(p-2)▽u),u∈X^(s)(R^(N)),u(x)>0,x∈R^(N).Where 1<p<N,N≥2,0<s<1,(-Δ)_(p)^(s) is the fractional p-Laplacian operator,the nonlinear term f:R×R^(N)→R is a continuous funtion which depends on the gradient term of the solution,V(x)is a positive continuous function.

关 键 词：分数阶椭圆方程 山路定理 迭代法 

分 类 号：O175[理学—数学]