Results 81 to 90 of about 208 (138)

Unique continuation for solutions of p(x)-Laplacian equations

Electronic Journal of Differential Equations, 2012
We study the unique continuation property for solutions to the quasilinear elliptic equation $$ hbox{div}(|abla u|^{p(x)-2}abla u) +V(x)|u|^{p(x)-2}u=0quad hbox{in }Omega, $$ where $Omega$ is a smooth bounded domain in $mathbb{R}^N$ and $1<p(x)&
Johnny Cuadro, Gabriel Lopez G.
doaj  

Nontrivial solutions for resonance quasilinear elliptic systems

Advances in Nonlinear Analysis
We establish an Amann-Zehnder-type result for resonance systems of quasilinear elliptic equations with homogeneous Dirichlet boundary conditions, involving nonlinearities growing asymptotically (p,q)\left(p,q)-linear at infinity.
Borgia Natalino, Cingolani Silvia, Vannella Giuseppina   +2 more
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Optimal $C^{1, \alpha}$ regularity for quasilinear elliptic equations with Orlicz growth

Electronic Journal of Qualitative Theory of Differential Equations
In this paper we obtain the interior optimal $C^{1, \alpha}$ regularity of weak solutions for the following quasilinear elliptic equations with Orlicz growth in divergence form \begin{equation*} -\operatorname{div}a(x, Du)=- \operatorname{div} \textbf{F}
Xiaohan Wang, Fengping Yao
doaj   +1 more source

Compactness Property of a Singular Quasilinear Elliptic Equation

Advanced Nonlinear Studies, 2008
Abstract We characterize a compactness property for a quasilinear equation with critical growth and singular term. Some applications of the compactness property are also pointed out.
openaire   +2 more sources

Multiple solutions for the $p$-Laplace equation with nonlinear boundary conditions

Electronic Journal of Differential Equations, 2006
In this note, we show the existence of at least three nontrivial solutions to the quasilinear elliptic equation $$ -Delta_p u + |u|^{p-2}u = f(x,u) $$ in a smooth bounded domain $Omega$ of $mathbb{R}^N$ with nonlinear boundary conditions $| abla ...
Julian Fernandez Bonder
doaj  

Multiplicity of weak solutions to degenerate weighted quasilinear elliptic equations with nonlocal terms and variable exponents

Electronic Journal of Qualitative Theory of Differential Equations
This paper studies the existence and multiplicity of weak solutions to degenerate weighted quasilinear elliptic equations with nonlocal nonlinearities and variable exponents.
Khaled Kefi
doaj   +1 more source

Multiple solutions for quasilinear elliptic equations with sign-changing potential

Electronic Journal of Differential Equations, 2016
In this article, we study the quasilinear elliptic equation $$ -\Delta_{p} u-(\Delta_{p}u^{2})u+ V (x)|u|^{p-2}u=g(x,u), \quad x\in \mathbb{R}^N, $$ where the potential V(x) and the nonlinearity g(x,u) are allowed to be sign-changing.
Ruimeng Wang, Kun Wang, Kaimin Teng
doaj  

On the Keldys-Fichera boundary-value problem for degenerate quasilinear elliptic equations

Electronic Journal of Differential Equations, 2002
We prove existence and uniqueness theorems for the Keldys-Fichera boundary-value problem using pseudo-monotone operators. The equation studied here is quasilinear, elliptic, and its set of degenerate points may be of non-zero measure.
Zu-Chi Chen, Benjin Xuan
doaj  

Existence and concentration of positive solutions for a quasilinear elliptic equation in R

Electronic Journal of Differential Equations, 2010
We study the existence and concentration of positive solutions for the quasilinear elliptic equation $$ -varepsilon^2u'' -varepsilon^2(u^2)''u+V(x) u = h(u) $$ in $mathbb{R}$ as $varepsilono 0$, where the potential $V:mathbb{R}o mathbb{R}$ has a ...
Elisandra Gloss
doaj  

The eigenvalue problem for a singular quasilinear elliptic equation

Electronic Journal of Differential Equations, 2004
We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega)$
Benjin Xuan
doaj