Results 81 to 90 of about 14,259 (205)

A singular ODE related to quasilinear elliptic equations

Electronic Journal of Differential Equations, 2000
We consider a quasilinear elliptic problem with the natural growth in the gradient. Existence, non-existence, uniqueness, and qualitative properties of positive solutions are obtained. We consider both weak and strong solutions.
Luka Korkut, Mervan Pasic, Darko Zubrinic   +2 more
doaj  

Norm Comparison Estimates for the Composite Operator

Journal of Function Spaces, 2014
This paper obtains the Lipschitz and BMO norm estimates for the composite operator 𝕄s∘P applied to differential forms. Here, 𝕄s is the Hardy-Littlewood maximal operator, and P is the potential operator.
Xuexin Li, Yong Wang, Yuming Xing
doaj   +1 more source

Nonlinear Dynamics and Auroral Acceleration Processes of Electrons Driven by Kinetic Alfvén Waves in the Magnetosphere

Journal of Geophysical Research: Space Physics, Volume 130, Issue 3, March 2025.
Abstract This study investigates the nonlinear Landau resonance and auroral acceleration processes of electrons driven by kinetic Alfvén waves (KAWs) in the Earth's magnetosphere. We analyze electron trajectories and parameters, such as kinetic energy, using test particle simulations, focusing on the transition between phase‐trapped and phase‐scattered
Koseki Saito, Yuto Katoh, Yohei Kawazura, Atsushi Kumamoto   +3 more
wiley   +1 more source

Quasilinear elliptic problems with nonstandard growth

Electronic Journal of Differential Equations, 2011
We prove the existence of solutions to Dirichlet problems associated with the $p(x)$-quasilinear elliptic equation $$ Au =- hbox{div} a(x,u,abla u)= f(x,u,abla u). $$ These solutions are obtained in Sobolev spaces with variable exponents.
Mohamed Badr Benboubker, Elhoussine Azroul, Abdelkrim Barbara   +2 more
doaj  

Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁

International Journal of Differential Equations, 2010
Assume that 𝑄 is a positive continuous function in ℝ𝑁 and satisfies some suitable conditions. We prove that the quasilinear elliptic equation −Δ𝑝𝑢+|𝑢|𝑝−2𝑢=𝑄(𝑧)|𝑢|𝑞−2𝑢 in ℝ𝑁 admits at least two solutions in ℝ𝑁 (one is a positive ground-state solution and ...
Huei-li Lin
doaj   +1 more source

Existence of Solutions for Quasilinear Elliptic Equations

Journal of Mathematical Analysis and Applications, 1997
Let \(\Omega\) be a bounded domain in \(\mathbb{R}^N\) with smooth boundary \(\partial\Omega\). The author uses variational methods to deduce sufficient conditions for the existence and multiplicity of weak solutions of the quasilinear Dirichlet problem: \[ -\text{div} \biggl(a \bigl(|\nabla u|^p \bigr)|\nabla u|^{p-2} \nabla u\biggr) =f(x,u) \quad ...
openaire   +1 more source

Multibump solutions for quasilinear elliptic equations

Journal of Functional Analysis, 2012
The article is concerned with constructing multibump type solution for quasilinear Schrödinger equations in the entire space. They get some extensions of the results of the classical work of \textit{V. Coti Zelati} and \textit{P. H. Rabinowitz} [Commun. Pure Appl. Math. 45, No.
Liu, Jia-Quan, Wang, Zhi-Qiang, Guo, Yu-Xia   +2 more
openaire   +1 more source

Quasilinear elliptic equations with natural growth

Differential and Integral Equations, 2007
In this paper we deal with the problem $$\left\{ \begin{array}{rcl} - {\rm div}\, (a(x,u)\nabla u) +{g(x,u,\nabla u)} & = & \lambda h(x)u + f{\mbox{ in }}\Omega,\\ u & = & 0{\mbox{ on }}\partial\Omega. \end{array} \right. $$ The main goal of the work is to get hypotheses on $a$, $g$ and $h$ such that the previous problem has a solution for all $\lambda>
ABDELLAOUI B, BOCCARDO, Lucio, PERAL I, PRIMO A.   +3 more
openaire   +3 more sources

Local renormalized solutions of elliptic equations with variable exponents in unbounded domains

Современная математика: Фундаментальные направления
In this paper, we consider a second-order quasilinear elliptic equation with variable nonlinearity exponents and a locally summable right-hand side.
L. M. Kozhevnikova
doaj   +1 more source

Eigenvalue problems for a quasilinear elliptic equation on ℝN

International Journal of Mathematics and Mathematical Sciences, 2005
We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation −Δpu=λg(x)|u|p−2u, x∈ℝN, lim|x|→+∞u(x)=0, where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator and the weight function g(x), being bounded ...
Marilena N. Poulou, Nikolaos M. Stavrakakis   +1 more
doaj   +1 more source