Results 31 to 40 of about 24,892 (124)

Equations involving fractional Laplacian operator: Compactness and application

, 2015
In this paper, we consider the following problem involving fractional Laplacian operator: \begin{equation}\label{eq:0.1} (-\Delta)^{\alpha} u= |u|^{2^*_\alpha-2-\varepsilon}u + \lambda u\,\, {\rm in}\,\, \Omega,\quad u=0 \,\, {\rm on}\, \, \partial\Omega,
Yan, Shusen, Yang, Jianfu, Yu, Xiaohui
core   +1 more source

A study and an application of the concentration compactness type principle

, 2019
In this article we develop a concentration compactness type principle in a variable exponent setup. As an application of this principle we discuss a problem involving fractional `{\it $(p(x),p^+)$-Laplacian}' and power nonlinearities with exponents $(p^+)^*$, $p_s^*(x)$ with the assumption that the critical set $\{x\in :p_s^*(x)=(p^+)^*\}$ is nonempty.
Panda, Akasmika, Choudhuri, Debajyoti
openaire   +2 more sources

Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent

, 2017
We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation \[ -{\Delta}u+ u=\big(I_\alpha*|u|^{\frac{\alpha}{N}+1}\big)|u|^{\frac{\alpha}{N}-1}u+f(x,u)\qquad \text{ in ...
Van Schaftingen, Jean, Xia, Jiankang
core   +1 more source

Lower Semicontinuity of Functionals via the Concentration-Compactness Principle

Journal of Mathematical Analysis and Applications, 2001
AbstractIn this paper we show the weak lower semicontinuity of some classes of functionals, using the concentration-compactness principle of P. L. Lions. These functionals involve an integral term, and we do not know whether it can be handled by the De Giorgi theorem.
openaire   +2 more sources

Concentration-Compactness Principle for Moser-type Inequalities in Lorentz-Sobolev Spaces

Potential Analysis, 2015
Let n ∈ 𝜖, n ≥ 2, q ∈ (1, ∞) and let ${\Omega }\subset \mathbb {R}^{n}$ be an open bounded set. We study the Concentration-Compactness Principle for the embedding of the Lorentz-Sobolev space
Li Dongliang, Zhu Maochun
openaire   +4 more sources

Looping dynamics of flexible chain with internal friction at different degree of compactness

, 2015
Recently single molecule experiments have shown the importance of internal friction in biopolymer dynamics. Such studies also suggested that the internal friction although independent of solvent viscosity has strong dependence on denaturant concentration.
Chakrabarti, Rajarshi, Samanta, Nairhita
core   +2 more sources

Nonlinear stabilitty for steady vortex pairs

, 2012
In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations.
A.L. Mazzucato, C. Marchioro, D. Pullin, E. Overman, E.H. Lieb, G.R. Burton, G.R. Burton, G.R. Burton, G.R. Burton, Geoffrey R. Burton, H.C. Pocklington, H.K. Moffatt, Helena J. Nussenzveig Lopes, J. Duc, J. Norbury, J. Yang, J. Yang, M.C. Lopes Filho, M.C. Lopes Filho, Milton C. Lopes Filho, P.-L. Lions, R. Pierrehumbert, R.J. DiPerna, R.J. Douglas, S. Agmon, Y.H. Wan   +25 more
core   +1 more source

EXISTENCE OF STEADY STATES FOR THE MAXWELL–SCHRÖDINGER–POISSON SYSTEM: EXPLORING THE APPLICABILITY OF THE CONCENTRATION–COMPACTNESS PRINCIPLE [PDF]

Mathematical Models and Methods in Applied Sciences, 2013
This paper reviews recent results and open problems concerning the existence of steady states to the Maxwell–Schrödinger system. A combination of tools, proofs and results are presented in the framework of the concentration–compactness method.
Catto, Isabelle, Dolbeault, Jean, Sánchez, Óscar, Soler, Juan   +3 more
openaire   +6 more sources

A simple derivation of BV bounds for inhomogeneous relaxation systems [PDF]

, 2014
We consider relaxation systems of transport equations with heterogeneous source terms and with boundary conditions, which limits are scalar conservation laws. Classical bounds fail in this context and in particular BV estimates.
Perthame, Benoit, Seguin, Nicolas, Tournus, Magali   +2 more
core   +2 more sources

Concentration-compactness principle for nonlocal scalar field equations with critical growth

Journal of Mathematical Analysis and Applications, 2017
The aim of this paper is to study a concentration-compactness principle for homogeneous fractional Sobolev space $\mathcal{D}^{s,2} (\mathbb{R}^N)$ for ...
João Marcos do Ó, Diego Ferraz
openaire   +3 more sources