Results 41 to 50 of about 31,246 (265)

Concentration and compactness in nonlinear Schrodinger-Poisson system with a general nonlinearity [PDF]

, 2009
In this paper we use a concentration and compactness argument to prove the existence of a nontrivial nonradial solution to the nonlinear Schrodinger-Poisson equations in R3, assuming on the nonlinearity the general hypotheses introduced by Berestycki ...
Azzollini, Antonio
core   +2 more sources

Concentration compactness principles for the systems of critical elliptic equations [PDF]

Differential Equations & Applications, 2012
In this paper, some important variants of the concentration compactness principle are established. By the variants, some kinds of the elliptic systems can be investigated and the existence of nontrivial solutions to the systems can be verified by the variational methods.
openaire   +2 more sources

Existence of Solutions to Fractional p-Laplacian Systems with Homogeneous Nonlinearities of Critical Sobolev Growth

Advanced Nonlinear Studies, 2020
In this paper, we investigate the existence of nontrivial solutions to the following fractional p-Laplacian system with homogeneous nonlinearities of critical Sobolev growth:
Lu Guozhen, Shen Yansheng
doaj   +1 more source

Concentration analysis and cocompactness [PDF]

, 2013
Loss of compactness that occurs in may significant PDE settings can be expressed in a well-structured form of profile decomposition for sequences. Profile decompositions are formulated in relation to a triplet $(X,Y,D)$, where $X$ and $Y$ are Banach ...
C Clark, C. Bennett, C.E. Kenig, E Lieb, G Arioli, G Kyriasis, G.B. Folland, H Bahouri, H Bahouri, H Bahouri, H Brezis, H Brezis, H. Bahouri, I Gallagher, I Schindler, I Schindler, I Schindler, J Ben Ameur, J Moser, J Shatah, J Shatah, K Tintarev, M Pino del, M Struwe, M. Biroli, M. Cwikel, P Gérard, P-L Lions, P-L Lions, P-L Lions, R DeVore, RA Adams, S Keraani, S Solimini, S. Jaffard, T Tao, T Tao, V. Benci, V.I. Yudovich, W.A. Strauss   +39 more
core   +1 more source

Concentration-Compactness Principle of Singular Trudinger--Moser Inequalities in ℝn and n-Laplace Equations

Advanced Nonlinear Studies, 2018
In this paper, we use the rearrangement-free argument, in the spirit of the work by Li, Lu and Zhu [25], on the concentration-compactness principle on the Heisenberg group to establish a sharpened version of the singular Lions concentration-compactness ...
Zhang Caifeng, Chen Lu
doaj   +1 more source

Multiple perturbations of a singular eigenvalue problem

, 2015
We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the concentration-compactness principle
Cencelj, Matija, Repovš, Dušan, Virk, Žiga   +2 more
core   +1 more source

Spectral optimization problems for potentials and measures [PDF]

, 2013
In the present paper we consider spectral optimization problems involving the Schr\"odinger operator $-\Delta +\mu$ on $\R^d$, the prototype being the minimization of the $k$ the eigenvalue $\lambda_k(\mu)$.
Bucur, Dorin, Buttazzo, Giuseppe, Velichkov, Bozhidar   +2 more
core   +4 more sources

The Existence of Positive Solution for Semilinear Elliptic Equations with Multiple an Inverse Square Potential and Hardy-Sobolev Critical Exponents

Abstract and Applied Analysis, 2019
Via the concentration compactness principle, delicate energy estimates, the strong maximum principle, and the Mountain Pass lemma, the existence of positive solutions for a nonlinear PDE with multi-singular inverse square potentials and critical Sobolev ...
M. Khiddi
doaj   +1 more source

Infinitely many solutions to quasilinear Schrödinger equations with critical exponent

Electronic Journal of Qualitative Theory of Differential Equations, 2019
This paper is concerned with the following quasilinear Schrödinger equations with critical exponent: \begin{equation*}\label{eqS0.1} - \Delta _p u+ V(x)|u|^{p-2}u - \Delta _p(|u|^{2\omega}) |u|^{2\omega-2}u = a k(x)|u|^{q-2}u+b |u|^{2\omega p^{*}-2}
Li Wang, Jixiu Wang, Xiongzheng Li
doaj   +1 more source

Existence of stable standing waves for the nonlinear Schrödinger equation with inverse-power potential and combined power-type and Choquard-type nonlinearities

AIMS Mathematics, 2021
In this paper, we investigate the existence of stable standing waves for the nonlinear Schr\"{o}dinger equation with inverse-power potential and combined power-type and Choquard-type nonlinearities \[ i \partial_t\psi+\triangle \psi+\frac{\gamma}{|x ...
Yile Wang
doaj   +1 more source