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
潘柔 1陈林2
作者信息
- 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
- 折叠
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)spu+V(x)up-2u = f(u,|▽u|p-2 ▽u),u ∈ Xs(RN),u(x)>0,∀x ∈RN.正解的存在性,其中1<p<N,N≥2,0<s<1,(-Δ)sp是分数阶p-拉普拉斯算子,非线性项f:R×RN→R是依赖于解的梯度项的连续函数,V(x)是正的连续函数.
Abstract
By using the mountain pass theorem and iterative methods to prove that the existence of positive solutions to the following frac-tional elliptic equation:{(-Δ)spu+V(x)up-2u = f(u,|▽u|p-2 ▽u),u ∈ Xs(RN),u(x)>0,∀x ∈RN.Where 1<p<N,N≥2,0<s<1,(-Δ)sp is the fractional p-Laplacian operator,the nonlinear termf:R×RN→Ris 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Key words
fractional elliptic equation/mountain pass theorem/iterative methods引用本文复制引用
基金项目
新疆维吾尔自治区自然科学基金资助项目(2022D01C459)
出版年
2024
NETL
NSTL
万方数据