Results 1 to 10 of about 89,789 (287)

On a Class of Quasilinear Elliptic Equations

Communications in Mathematical Research, 2023
Summary: We consider a class of quasilinear elliptic boundary problems, including the following Modified Nonlinear Schrödinger Equation as a special case: \[ \begin{cases} \Delta u+ \frac{1}{2} u \Delta (u^2) -V(x) u+|u|^{q -2} u=0\quad &\text{in } \Omega, \\ u=0\quad &\text{on }\partial \Omega, \end{cases} \] where \(\Omega\) is the entire space ...
Sayed Hamid Hashimi, Zhi-Qiang Wang null, Lin Zhang   +2 more
semanticscholar   +2 more sources

Compactness methods for Hölder estimates of certain degenerate elliptic equations [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2012
In this paper we obtain the interior $C^{1,\alpha}$ regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local $L^\infty$ estimates and weak Harnack inequality for second-order linear elliptic equations,
Fengping Yao, Mijia Lai, Huilian Jia
doaj   +3 more sources

Quasilinear elliptic Hamilton-Jacobi equations on complete manifolds [PDF]

Comptes Rendus. Mathématique, 2013
Let (Mn,g) be an n-dimensional complete, non-compact and connected Riemannian manifold, with Ricci tensor Riccg and sectional curvature Secg. Assume Riccg⩾(1−n)B2, and either p>2 and Secg(x)=o(dist2(x,a)) when dist2(x,a)→∞ for a∈M, or 1<p<2 and Secg(x)⩽0.
Marie‐Françoise Bidaut‐Véron, Marta García‐Huidobro, Лаурент Верон   +2 more
openalex   +7 more sources

The Calderón problem for quasilinear elliptic equations

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2020
In this paper we show uniqueness of the conductivity for the quasilinear Calderón's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions on the direct problem, a real-valued conductivity allowing a small analytic continuation to the complex plane induce ...
Claudio Muñoz, G. Uhlmann
semanticscholar   +5 more sources

Quasilinear elliptic equations with natural growth and quasilinear elliptic equations with singular drift [PDF]

Nonlinear Analysis, 2018
11 ...
Marco Degiovanni, M. Marzocchi
semanticscholar   +5 more sources

Existence and concentration behavior of solutions for a class of quasilinear elliptic equations with critical growth

Advances in Nonlinear Analysis, 2017
In this paper, we study a class of quasilinear elliptic equations involving the Sobolev critical ...
Teng Kaimin, Yang Xiaofeng
doaj   +2 more sources

On singular quasilinear elliptic equations with data measures

Advances in Nonlinear Analysis, 2021
The aim of this work is to study a quasilinear elliptic equation with singular nonlinearity and data measure. Existence and non-existence results are obtained under necessary or sufficient conditions on the data, where the main ingredient is the ...
Alaa Nour Eddine, Aqel Fatima, Taourirte Laila   +2 more
doaj   +2 more sources

Solutions to singular quasilinear elliptic equations on bounded domains

Electronic Journal of Differential Equations, 2018
In this article we study quasilinear elliptic equations with a singular operator and at critical Sobolev growth. We prove the existence of positive solutions.
Zhouxin Li, Youjun Wang
doaj   +1 more source

Quasilinear elliptic equations with critical potentials

Advances in Nonlinear Analysis, 2017
We study Liouville theorems for problems of the ...
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj   +2 more sources

Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents

AIMS Mathematics
This paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term.
Khaled Kefi, Nasser S. Albalawi
doaj   +2 more sources