Results 11 to 20 of about 416 (68)

Flat solutions of the 1-Laplacian equation [PDF]

, 2017
For every $f \in L^N(\Omega)$ defined in an open bounded subset $\Omega$ of $\mathbb{R}^N$, we prove that a solution $u \in W_0^{1, 1}(\Omega)$ of the $1$-Laplacian equation ${-}\mathrm{div}{(\frac{\nabla u}{|\nabla u|})} = f$ in $\Omega$ satisfies ...
Orsina, Luigi, Ponce, Augusto C.
core   +3 more sources

Measure Data Problems for a Class of Elliptic Equations with Mixed Absorption-Reaction

Advanced Nonlinear Studies, 2021
In the present paper, we study the existence of nonnegative solutions to the Dirichlet problem ℒp,qM⁢u:=-Δ⁢u+up-M⁢|∇⁡u|q=μ{{\mathcal{L}}^{{M}}_{p,q}u:=-\Delta u+u^{p}-M|\nabla u|^{q}=\mu} in a domain Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} where μ is a ...
Bidaut-Véron Marie-Françoise, Garcia-Huidobro Marta, Véron Laurent   +2 more
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N-Laplacian critical problem with discontinuous nonlinearities

Advances in Nonlinear Analysis, 2015
In this paper, we study the existence of a solution of the N-Laplacian critical problem with discontinuous nonlinearity of Heaviside type in a smooth bounded domain with respect to a positive parameter λ.
Tiwari Sweta
doaj   +1 more source

A variant of Clark’s theorem and its applications for nonsmooth functionals without the global symmetric condition

Advances in Nonlinear Analysis, 2021
We give a new non-smooth Clark’s theorem without the global symmetric condition. The theorem can be applied to generalized quasi-linear elliptic equations with small continous perturbations.
Huang Chen
doaj   +1 more source

Bifurcation analysis for a modified quasilinear equation with negative exponent

Advances in Nonlinear Analysis, 2021
In this paper, we consider the following modified quasilinear problem:
Chen Siyu, Santos Carlos Alberto, Yang Minbo, Zhou Jiazheng   +3 more
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Quasilinear equations with indefinite nonlinearity

Advances in Nonlinear Analysis, 2018
In this paper, we are concerned with quasilinear equations with indefinite nonlinearity and explore the existence of infinitely many solutions.
Zhao Junfang, Liu Xiangqing, Feng Zhaosheng   +2 more
doaj   +1 more source

On sufficient “local” conditions for existence results to generalized p(.)-Laplace equations involving critical growth

Advances in Nonlinear Analysis, 2022
In this article, we study the existence of multiple solutions to a generalized p(⋅)p\left(\cdot )-Laplace equation with two parameters involving critical growth.
Ho Ky, Sim Inbo
doaj   +1 more source

On the symmetry of minimizers in constrained quasi-linear problems [PDF]

, 2010
We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems.Comment: 18 ...
Squassina, Marco
core   +1 more source

Isolated singularities of the prescribed mean curvature equation in Minkowski $3$-space [PDF]

, 2017
We give a classification of non-removable isolated singularities for real analytic solutions of the prescribed mean curvature equation in Minkowski $3 ...
Gálvez, José A., Jiménez, Asun, Mira, Pablo   +2 more
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A non-smooth Brezis-Oswald uniqueness result

Open Mathematics, 2023
We classify the non-negative critical points in W01,p(Ω){W}_{0}^{1,p}\left(\Omega ) of J(v)=∫ΩH(Dv)−F(x,v)dx,J\left(v)=\mathop{\int }\limits_{\Omega }\hspace{0.15em}H\left(Dv)-F\left(x,v){\rm{d}}x, where HH is convex and positively pp-homogeneous, while ...
Mosconi Sunra
doaj   +1 more source