Results 41 to 50 of about 383 (68)

Nonoccurrence of Lavrentiev gap for a class of functionals with nonstandard growth

Advances in Nonlinear Analysis
We consider the functional ℱ(u)≔∫Ωf(x,Du(x))dx,{\mathcal{ {\mathcal F} }}\left(u):= \mathop{\int }\limits_{\Omega }f\left(x,Du\left(x)){\rm{d}}x, where f(x,z)f\left(x,z) satisfies a (p,q)\left(p,q)-growth condition with respect to zz and can be ...
De Filippis Filomena, Leonetti Francesco, Treu Giulia   +2 more
doaj   +1 more source

On the H\'enon-Lane-Emden conjecture [PDF]

, 2011
We consider Liouville-type theorems for the following H\'{e}non-Lane-Emden system \hfill -\Delta u&=& |x|^{a}v^p \text{in} \mathbb{R}^N, \hfill -\Delta v&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when $pq>1$, $p,q,a,b\ge0$.
In R, In R N, Mostafa Fazly, Nassif Ghoussoub   +3 more
core   +1 more source

k-convex solutions for multiparameter Dirichlet systems with k-Hessian operator and Lane-Emden type nonlinearities

Advances in Nonlinear Analysis
In this article, our main aim is to investigate the existence of radial kk-convex solutions for the following Dirichlet system with kk-Hessian operators: Sk(D2u)=λ1ν1(∣x∣)(−u)p1(−v)q1inℬ(R),Sk(D2v)=λ2ν2(∣x∣)(−u)p2(−v)q2inℬ(R),u=v=0on∂ℬ(R).\left\{\begin ...
He Xingyue, Gao Chenghua, Wang Jingjing
doaj   +1 more source

Segregated solutions for nonlinear Schrödinger systems with a large number of components

Advanced Nonlinear Studies
In this paper we are concerned with the existence of segregated non-radial solutions for nonlinear Schrödinger systems with a large number of components in a weak fully attractive or repulsive regime in presence of a suitable external radial potential.
Chen Haixia, Pistoia Angela
doaj   +1 more source

Asymptotic behaviors of least energy solutions for weakly coupled nonlinear Schrödinger systems

Advanced Nonlinear Studies
We study the asymptotic behavior of positive least energy solutions to the weakly coupled nonlinear Schrödinger systems with nearly critical exponents.
Chen Zhijie, Cheng Zetao
doaj   +1 more source

Synchronized vector solutions for the nonlinear Hartree system with nonlocal interaction

Advanced Nonlinear Studies
We are concerned with the following nonlinear Hartree system−Δu+P1(|x|)u=α1|x|−1∗u2u+β|x|−1∗v2u inR3,−Δv+P2(|x|)v=α2|x|−1∗v2v+β|x|−1∗u2v inR3, $$\begin{cases}-{\Delta}u+{P}_{1}\left(\vert x\vert \right)u={\alpha }_{1}\left(\vert x{\vert }^{-1}\ast {u}^{2}
Gao Fashun, Yang Minbo, Zhao Shunneng
doaj   +1 more source

Nonlinear elliptic equations and systems with linear part at resonance

, 2016
The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues.
Korman, Philip
core   +1 more source

Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy-Sobolev exponent and singular nonlinearity. [PDF]

J Inequal Appl, 2018
Shen L.
europepmc   +1 more source

Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian. [PDF]

J Inequal Appl, 2018
Shen L.
europepmc   +1 more source

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Anisotropic nonlinear elliptic systems with variable exponents and degenerate coercivity

Applicable Analysis, 2021
Fares Mokhtari
exaly