Results 41 to 50 of about 33,828 (297)

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

Existence of solutions for critical systems with variable exponents

Mathematical Modelling and Analysis, 2018
In this work, we deal with elliptic systems under critical growth conditions on the nonlinearities. Using a variant of concentration-compactness principle, we prove an existence result.
Hadjira Lalilia, Saadia Tas, Ali Djellit
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

Lack of compactness in the 2D critical Sobolev embedding, the general case [PDF]

, 2011
This paper is devoted to the description of the lack of compactness of the Sobolev embedding of $H^1(\R^2)$ in the critical Orlicz space ${\cL}(\R^2)$.
Bahouri, Hajer, Majdoub, Mohamed, Masmoudi, Nader   +2 more
core   +8 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

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

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

A multiplicity result for the scalar field equation

, 2013
We prove the existence of $N - 1$ distinct pairs of nontrivial solutions of the scalar field equation in ${\mathbb R}^N$ under a slow decay condition on the potential near infinity, without any symmetry assumptions.
Perera, Kanishka
core   +1 more source

Revealing the structure of land plant photosystem II: the journey from negative‐stain EM to cryo‐EM

FEBS Letters, EarlyView.
Advances in cryo‐EM have revealed the detailed structure of Photosystem II, a key protein complex driving photosynthesis. This review traces the journey from early low‐resolution images to high‐resolution models, highlighting how these discoveries deepen our understanding of light harvesting and energy conversion in plants.
Roman Kouřil
wiley   +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