Concentration-compactness principle of singular Trudinger–Moser inequality involving N-Finsler–Laplacian operator [PDF]
International Journal of Mathematics, 2020 In this paper, suppose [Formula: see text] be a convex function of class [Formula: see text] which is even and positively homogeneous of degree 1. We establish the Lions type concentration-compactness principle of singular Trudinger–Moser Inequalities involving [Formula: see text]-Finsler–Laplacian operator.
Yanjun Liu
openalex +5 more sources
Concentration-Compactness Principle for Generalized Trudinger Inequalities
Zeitschrift für Analysis und ihre Anwendungen, 2011 Let \Omega\subset\mathbb R^n , n\geq 2 , be a bounded domain and let \alpha < n-1 . We prove the Concentration-Compactness Principle for the embedding of the Orlicz-Sobolev space
Robert Černý +2 more
openalex +4 more sources
Existence for (p, q) critical systems in the Heisenberg group [PDF]
Advances in Nonlinear Analysis, 2019 This paper deals with the existence of entire nontrivial solutions for critical quasilinear systems (𝓢) in the Heisenberg group ℍn, driven by general (p, q) elliptic operators of Marcellini types.
Pucci Patrizia, Temperini Letizia
doaj +2 more sources
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.
Akasmika Panda, Debajyoti Choudhuri
openalex +4 more sources
Infinitely many solutions for the p-fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity [PDF]
Nonlinear Analysis, 2018 In this paper, we consider the fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity. By means of the concentration-compactness principle in fractional Sobolev space and the Kajikiya's new version of the symmetric mountain ...
Sihua Liang, Jihui Zhang
doaj +3 more sources
Journal of Differential Equations, 2002 AbstractFor a bounded domain Ω⊂R2, we establish a concentration-compactness result for the following class of “singular” Liouville equations:−Δu=eu−4π∑j=1mαjδpj in Ω where pj∈Ω, αj>0 and δpj denotes the Dirac measure with pole at point pj, j=1,…,m. Our result extends Brezis–Merle's theorem (Comm.
Daniele Bartolucci, Gabriella Tarantello
openalex +4 more sources
The concentration-compactness principle for the nonlocal anisotropic
Nonlinear Analysis, 2023 19 ...
Jamil Chaker +2 more
openalex +4 more sources
A CONCENTRATION-COMPACTNESS PRINCIPLE FOR PERTURBED ISOPERIMETRIC PROBLEMS WITH GENERAL ASSUMPTIONS
Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article and under mild assumptions we establish existence and density estimates of generalized minimizers of perturbed ...
Jules Candau-Tilh
openalex +5 more sources
Concentration-compactness principle for nonlocal scalar field equations with critical growth
Journal of Mathematical Analysis and Applications, 2016 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
openalex +4 more sources
Concentration-compactness principle for Trudinger-Moser inequalities on Heisenberg Groups and existence of ground state solutions [PDF]
Calculus of Variations and Partial Differential Equations, 2017 Let $\mathbb{H}^{n}=\mathbb{C}^{n}\times\mathbb{R}$ be the $n$-dimensional Heisenberg group, $Q=2n+2$ be the homogeneous dimension of $\mathbb{H}^{n}$. We extend the well-known concentration-compactness principle on finite domains in the Euclidean spaces of \ P. L. Lions to the setting of the Heisenberg group $\mathbb{H}^{n}$.
Jungang Li, Guozhen Lu, Maochun Zhu
openalex +5 more sources