Journal of Differential Geometry, ISSN 0022-040X, 2009, Volume 81, Issue 2, pp. 225 - 250

Let n be an integer such that 25 <= n <= 51. We construct a smooth metric g on S-n with the property that the set of constant scalar curvature metrics in the...

MATHEMATICS | COMPACTNESS

MATHEMATICS | COMPACTNESS

Journal Article

Expositiones Mathematicae, ISSN 0723-0869, 2010, Volume 28, Issue 4, pp. 385 - 394

We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their...

Compactness in Lp | Kolmogorov–Riesz compactness theorem | Compactness in L | Kolmogorov-Riesz compactness theorem | MATHEMATICS | Compactness in L-P

Compactness in Lp | Kolmogorov–Riesz compactness theorem | Compactness in L | Kolmogorov-Riesz compactness theorem | MATHEMATICS | Compactness in L-P

Journal Article

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, ISSN 0294-1449, Volume 10, Issue 4, pp. 405 - 412

We prove that the only probability measures supported at connected subsets of 2 × 2 matrices without rank-one connections and commuting with the determinant...

compactness | regularity | Young measures

compactness | regularity | Young measures

Journal Article

Information Sciences, ISSN 0020-0255, 2005, Volume 173, Issue 1, pp. 35 - 48

In this paper, a new notion of compactness is introduced in L-topological spaces by means of β a -open cover and Q a -open cover, which is called S...

Fuzzy compactness | N-compactness | S∗-compactness | Qa-open cover | Strong compactness | Ultra-compactness | L-topology | βa-open cover | compactness | open cover | Q(a)-open cover | beta(a)-open cover | NETS | fuzzy compactness | strong compactness | S-compactness | ultra-compactness | COMPUTER SCIENCE, INFORMATION SYSTEMS

Fuzzy compactness | N-compactness | S∗-compactness | Qa-open cover | Strong compactness | Ultra-compactness | L-topology | βa-open cover | compactness | open cover | Q(a)-open cover | beta(a)-open cover | NETS | fuzzy compactness | strong compactness | S-compactness | ultra-compactness | COMPUTER SCIENCE, INFORMATION SYSTEMS

Journal Article

Expositiones Mathematicae, ISSN 0723-0869, 03/2019, Volume 37, Issue 1, pp. 84 - 91

The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical...

Kolmogorov–Riesz compactness theorem | Compactness in [formula omitted] | Compactness in L | MATHEMATICS | Kolmogorov-Riesz compactness theorem | Compactness in L-P | SPACES | Mathematics - Functional Analysis

Kolmogorov–Riesz compactness theorem | Compactness in [formula omitted] | Compactness in L | MATHEMATICS | Kolmogorov-Riesz compactness theorem | Compactness in L-P | SPACES | Mathematics - Functional Analysis

Journal Article

2012, ISBN 3110276402, xii, 339

Book

Journal of Functional Analysis, ISSN 0022-1236, 07/2016, Volume 271, Issue 1, pp. 107 - 135

We consider the general Choquard equations−Δu+u=(Iα⁎|u|p)|u|p−2u where Iα is a Riesz potential. We construct minimal action odd solutions for p∈(N+αN,N+αN−2)...

Concentration–compactness | Stationary nonlinear Schrödinger–Newton equation | Stationary Hartree equation | Nodal Nehari set | Stationary nonlinear Schrödinger-Newton equation | Concentration-compactness | EXISTENCE | MATHEMATICS | Stationary nonlinear | SYMMETRIZATION | PRINCIPLE | Schrodinger-Newton equation | Cytokinins | Mathematics - Analysis of PDEs

Concentration–compactness | Stationary nonlinear Schrödinger–Newton equation | Stationary Hartree equation | Nodal Nehari set | Stationary nonlinear Schrödinger-Newton equation | Concentration-compactness | EXISTENCE | MATHEMATICS | Stationary nonlinear | SYMMETRIZATION | PRINCIPLE | Schrodinger-Newton equation | Cytokinins | Mathematics - Analysis of PDEs

Journal Article

Commentationes Mathematicae Universitatis Carolinae, ISSN 0010-2628, 2018, Volume 59, Issue 4, pp. 513 - 521

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 04/2012, Volume 75, Issue 6, pp. 3072 - 3077

A strong compactness result in the spirit of the Lions–Aubin–Simon lemma is proven for piecewise constant functions in time (uτ) with values in a Banach space....

Aubin lemma | Rothe method | Compactness

Aubin lemma | Rothe method | Compactness

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2011, Volume 363, Issue 7, pp. 3639 - 3663

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2017, Volume 145, Issue 2, pp. 737 - 747

where I_\alpha is the Riesz potential of order \alpha \in (0,N). The solution is constructed as the limit of minimal action nodal solutions for the nonlinear...

Stationary nonlinear Schrödinger-Newton equation | Concentration-compactness | Stationary Hartree equation | Nodal Nehari set | Stationary nonlinear Schrodinger-Newton equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | nodal Nehari set | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | stationary Hartree equation | compactness | concentration | GROUND-STATES | Mathematics - Analysis of PDEs

Stationary nonlinear Schrödinger-Newton equation | Concentration-compactness | Stationary Hartree equation | Nodal Nehari set | Stationary nonlinear Schrodinger-Newton equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | nodal Nehari set | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | stationary Hartree equation | compactness | concentration | GROUND-STATES | Mathematics - Analysis of PDEs

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 346, Issue 1, pp. 155 - 169

In this paper, we are concerned with the system of Schrödinger–Poisson equations (*) { − Δ u + V ( x ) u + ϕ u = f ( x , u ) , in R 3 , − Δ ϕ = u 2 , in R 3 ....

Concentration–compactness principle | Ground state solution | Variational methods | Pohozaev identity | variational methods | SYSTEM | MATHEMATICS | POSITIVE SOLUTION | MATHEMATICS, APPLIED | STATES | ground state solution | MAXWELL EQUATIONS | concentration-compactness principle | PRINCIPLE | Concentration-compactness principle

Concentration–compactness principle | Ground state solution | Variational methods | Pohozaev identity | variational methods | SYSTEM | MATHEMATICS | POSITIVE SOLUTION | MATHEMATICS, APPLIED | STATES | ground state solution | MAXWELL EQUATIONS | concentration-compactness principle | PRINCIPLE | Concentration-compactness principle

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2018, Volume 457, Issue 1, pp. 233 - 247

We prove that a smooth bounded pseudoconvex domain Ω⊆C3 with a one-dimensional complex manifold M in its boundary has a noncompact ∂‾-Neumann operator on...

Compactness of the [formula omitted]-Neumann operator | Pseudoconvex domains | Bergman kernels | Compactness of the ∂‾-Neumann operator

Compactness of the [formula omitted]-Neumann operator | Pseudoconvex domains | Bergman kernels | Compactness of the ∂‾-Neumann operator

Journal Article

ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 2018, Volume 24, Issue 1, pp. 1 - 24

We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent...

Fractional magnetic operators | Minimization problems | Concentration compactness | EXISTENCE | MATHEMATICS, APPLIED | INEQUALITIES | concentration compactness | ELECTROMAGNETIC-FIELDS | SOBOLEV SPACES | SYMMETRY | minimization problems | COMPACTNESS | EQUATION | SEMICLASSICAL LIMIT | AUTOMATION & CONTROL SYSTEMS | SCHRODINGER-OPERATORS

Fractional magnetic operators | Minimization problems | Concentration compactness | EXISTENCE | MATHEMATICS, APPLIED | INEQUALITIES | concentration compactness | ELECTROMAGNETIC-FIELDS | SOBOLEV SPACES | SYMMETRY | minimization problems | COMPACTNESS | EQUATION | SEMICLASSICAL LIMIT | AUTOMATION & CONTROL SYSTEMS | SCHRODINGER-OPERATORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 2, pp. 1267 - 1283

We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop–Phelp's theorem and James' compactness...

Weakly compact | James' compactness theorem | MATHEMATICS | WEAK COMPACTNESS | MATHEMATICS, APPLIED | BOUNDARIES | CONVEX-SETS

Weakly compact | James' compactness theorem | MATHEMATICS | WEAK COMPACTNESS | MATHEMATICS, APPLIED | BOUNDARIES | CONVEX-SETS

Journal Article

Analysis and PDE, ISSN 2157-5045, 2018, Volume 12, Issue 4, pp. 1049 - 1063

Journal Article

Algebra and Logic, ISSN 0002-5232, 5/2016, Volume 55, Issue 2, pp. 146 - 172

Different types of compactness in the Zariski topology are explored: for instance, equational Noetherianity, equational Artinianity, qω-compactness, and...

metacompact algebras | equationally Artinian algebras | equationally Noetherian algebras | Mathematics | u ω -compactness | algebraic sets | q ω -compactness | equations | algebraic structures | coordinate algebra | Algebra | varieties | radical ideal | equational domains | free algebras | Zariski topology | metacompact spaces | prevarieties | Mathematical Logic and Foundations | Hilbert’s basis theorem | compactness | ELEMENTARY THEORY | q(omega)-compactness | LOGIC | Hilbert's basis theorem | MATHEMATICS | THEOREMS | u(omega)-compactness | Analysis | Geometry, Algebraic

metacompact algebras | equationally Artinian algebras | equationally Noetherian algebras | Mathematics | u ω -compactness | algebraic sets | q ω -compactness | equations | algebraic structures | coordinate algebra | Algebra | varieties | radical ideal | equational domains | free algebras | Zariski topology | metacompact spaces | prevarieties | Mathematical Logic and Foundations | Hilbert’s basis theorem | compactness | ELEMENTARY THEORY | q(omega)-compactness | LOGIC | Hilbert's basis theorem | MATHEMATICS | THEOREMS | u(omega)-compactness | Analysis | Geometry, Algebraic

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 02/2016, Volume 260, Issue 4, pp. 3658 - 3690

We prove (see Theorem 1.1) that the Lin–Ni conjecture for closed manifolds is false in dimensions n=4,5 when the scalar curvature is negative, but that it...

MATHEMATICS | ELLIPTIC-EQUATIONS | COMPACTNESS | UNIQUENESS

MATHEMATICS | ELLIPTIC-EQUATIONS | COMPACTNESS | UNIQUENESS

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2014, Volume 46, Issue 1, pp. 939 - 997

Journal Article

Order, ISSN 0167-8094, 7/2016, Volume 33, Issue 2, pp. 269 - 287

We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for...

Ultrafilter convergence | Compactness | Linearly ordered | Mathematics | Theory of Computation | (pseudo-)gap | Pseudocompactness | Decomposable | Descendingly complete | λ-boundedness | Geometry | (weak) initial λ-compactness | Generalized ordered topological space | Converging ν-sequence | Discrete Mathematics in Computer Science | Complete accumulation point | Regular ultrafilter | (weak) [ν, ν]-compactness | lambda-boundedness | (weak) initial lambda-compactness | Converging.-sequence | MATHEMATICS | COMPACT | (weak) [nu.nu]-compactness | Mathematics - General Topology

Ultrafilter convergence | Compactness | Linearly ordered | Mathematics | Theory of Computation | (pseudo-)gap | Pseudocompactness | Decomposable | Descendingly complete | λ-boundedness | Geometry | (weak) initial λ-compactness | Generalized ordered topological space | Converging ν-sequence | Discrete Mathematics in Computer Science | Complete accumulation point | Regular ultrafilter | (weak) [ν, ν]-compactness | lambda-boundedness | (weak) initial lambda-compactness | Converging.-sequence | MATHEMATICS | COMPACT | (weak) [nu.nu]-compactness | Mathematics - General Topology

Journal Article

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