关于一类(p(u),q(u))-Laplacian问题
On a Class of (p(u),q(u))-Laplacian Problem
DOI: 10.12677/PM.2021.114072, PDF,   
作者: 李燕茹：上海理工大学理学院，上海
关键词: (p(u)；q(u))-Laplacian；存在性；唯一性；(p(u)；q(u))-Laplacian； Existence； Uniqueness
摘要: 本文在(p(u),q(u))为局部的情况下考虑下列变量指数椭圆方程的存在性：其中Ω ⊂ ℝd (d ≥ 2)是一个光滑有界区域， f ( x)是给定的函数并且p,q : ℝ →[1,+∞)为变指数函数，利用了扰动技术及不动点定理证明(p(u),q(u))-Laplacian方程在(p(u),q(u))为局部的情况下弱解的存在性。
Abstract: In this paper, we consider the existence of the following variable exponent elliptic problem when(p(u),q(u)) is a local quantity: where Ω ⊂ ℝd (d ≥ 2) is a smooth bounded domain, f ( x) is a given data, p,q : ℝ →[1,+∞) are exponent functions. We obtain the existence of weak solution of (p(u),q(u)) -Laplacian, (p(u),q(u)) is a local quantity by means of singular perturbation technique and Schauder fixed point theorem.
文章引用：李燕茹. 关于一类(p(u),q(u))-Laplacian问题[J]. 理论数学, 2021, 11(4): 586-598. https://doi.org/10.12677/PM.2021.114072

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