Existence and Asymptotic Behavior of Boundary Blow-Up Solutions for Weightedp(x)-Laplacian Equations with Exponential Nonlinearities

LiYin; YunruiGuo; JingYang; BiboLu; QihuZhang

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Existence and Asymptotic Behavior of Boundary Blow-Up Solutions for Weightedp(x)-Laplacian Equations with Exponential Nonlinearities

机译：具有指数非线性的加权p（x）-Laplacian方程边界爆破解的存在性与渐近行为

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This paper investigates the followingp(x)-Laplacian equations with exponential nonlinearities:−Δp(x)u+ρ(x)ef(x,u)=0inΩ,u(x)→+∞asd(x,∂Ω)→0, where−Δp(x)u=−div(|∇u|p(x)−2∇u)is calledp(x)-Laplacian,ρ(x)∈C(Ω). The asymptotic behavior of boundary blow-up solutions is discussed, and the existence of boundary blow-up solutions is given.

机译：本文研究具有指数非线性的以下p（x）-Laplacian方程：-Δp（x）u +ρ（x）ef（x，u）=0inΩ，u（x）→+∞asd（x，∂Ω）→ 0，其中-Δp（x）u = -div（|∇u| p（x）-2∇u）被称为p（x）-Laplacian，ρ（x）∈C（Ω）。讨论了边界爆破解的渐近性质，并给出了边界爆破解的存在性。

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《Abstract and applied analysis》 |2010年第3期|共20页
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LiYin; YunruiGuo; JingYang; BiboLu; QihuZhang;
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1. Boundary Blow-Up Solutions to -Laplacian Equations with Exponential Nonlinearities [J] . Qihu Zhang Journal of inequalities and applications . 2007,第1期

机译：具有指数非线性的-Laplacian方程的边界爆破解
2. The exact asymptotic behavior of boundary blow-up solutions to infinity Laplacian equations [J] . Wan Haitao ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees . 2016,第4期

机译：无穷拉普拉斯方程组的边界爆破解的精确渐近行为
3. Existence and Asymptotic Behavior of Boundary Blow-Up Weak Solutions for Problems Involving the p-Laplacian [J] . BELHAJ RHOUMA Nedra, DRISSI Amor, SAYEB Wahid 偏微分方程：英文版 . 2013,第002期

机译：关于p-Laplacian问题的边界爆破弱解的存在性与渐近行为
4. Global existence and blow-up solutions for a class of nonlinear reaction diffusion equations under nonlinear boundary flux [C] . Yang Yan, Zhang Lingling Chinese Control and Decision Conference . 2019

机译：非线性边界通量下一类非线性反应扩散方程的整体存在和爆破解
5. Normalized p-laplacian evolution: boundary behavior of non-negative solutions of fully nonlinear parabolic equations: Gradient bounds for p-harmonic systems with vanishing neumann (dirichlet) data in a convex domain. [D] . Banerjee, Agnid. 2014

机译：归一化的p-拉普拉斯演化：完全非线性抛物方程的非负解的边界行为：具有在凸域中消失的Neumann（dirichlet）数据的p调和系统的梯度界。
6. Global existence and blow-up results for p-Laplacian parabolic problems under nonlinear boundary conditions [O] . Juntang Ding -1

机译：非线性边界条件下p-Laplacian抛物型问题的整体存在和爆破结果
7. Boundary Blow-Up Solutions to p(x)-Laplacian Equations with Exponential Nonlinearities [O] . Qihu Zhang 2008

机译：具有指数非线性的p（x）-Laplacian方程的边界爆破解

Existence and Asymptotic Behavior of Boundary Blow-Up Solutions for Weightedp(x)-Laplacian Equations with Exponential Nonlinearities

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