Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2014, Volume 414, Issue 1, pp. 372 - 385

By exploiting a suitable Trudinger–Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of...

Fractional Laplacian | Nonlocal equations | Trudinger–Moser inequality | Trudinger-Moser inequality

Fractional Laplacian | Nonlocal equations | Trudinger–Moser inequality | Trudinger-Moser inequality

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 03/2020, Volume 192, p. 111661

We obtain approximate convexity principles for solutions to some classes of nonlinear elliptic partial differential equations in convex domains involving...

Maximum principles | Convexity | Elliptic PDEs | Concavity

Maximum principles | Convexity | Elliptic PDEs | Concavity

Journal Article

Comptes Rendus Mathematique, ISSN 1631-073X, 07/2016, Volume 354, Issue 8, pp. 825 - 831

We prove a Bourgain–Brézis–Mironescu-type formula for a class of nonlocal magnetic spaces, which builds a bridge between a fractional magnetic 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

2016, UNITEXT, ISBN 9788847057906, Volume 96

Il testo è stato concepito per la struttura degli attuali corsi di laurea in Biologia, Matematica, Matematica Applicata, Ingegneria, Scienze Naturali e...

Engineering mathematics | Applied mathematics | Differential equations | Mathematics | Biomathematics | Mathematical physics

Engineering mathematics | Applied mathematics | Differential equations | Mathematics | Biomathematics | Mathematical physics

Web Resource

2016, UNITEXT, ISBN 9788847057906, Volume 96

Il testo è stato concepito per la struttura degli attuali corsi di laurea in Biologia, Matematica, Matematica Applicata, Ingegneria, Scienze Naturali e...

Engineering mathematics | Applied mathematics | Differential equations | Mathematics | Biomathematics | Mathematical physics

Engineering mathematics | Applied mathematics | Differential equations | Mathematics | Biomathematics | Mathematical physics

Web Resource

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 06/2017, Volume 56, Issue 3

Journal Article

Journal d'Analyse Mathématique, ISSN 0021-7670, 10/2019, Volume 139, Issue 2, pp. 773 - 797

We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex...

Dirichlet problem | Sobolev space | Continuity (mathematics) | Inequalities

Dirichlet problem | Sobolev space | Continuity (mathematics) | Inequalities

Journal Article

Discrete and Continuous Dynamical Systems - Series S, ISSN 1937-1632, 06/2018, Volume 11, Issue 3, pp. i - I

Journal Article

Advances in Calculus of Variations, ISSN 1864-8258, 04/2016, Volume 9, Issue 2, pp. 101 - 125

We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in...

Morse theory | regularity of solutions | 35P15 | 35R11 | Fractional | existence and multiplicity of weak solutions | 35P30 | Laplacian problems | Fractional p-Laplacian problems | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | REGULARITY | DIRICHLET PROBLEM | GUIDE | Game theory | Population biology | Phase transitions | Dynamic tests | Phase transformations | Dynamics | Mathematical analysis | Continuum mechanics | Topology | Calculus of variations

Morse theory | regularity of solutions | 35P15 | 35R11 | Fractional | existence and multiplicity of weak solutions | 35P30 | Laplacian problems | Fractional p-Laplacian problems | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | REGULARITY | DIRICHLET PROBLEM | GUIDE | Game theory | Population biology | Phase transitions | Dynamic tests | Phase transformations | Dynamics | Mathematical analysis | Continuum mechanics | Topology | Calculus of variations

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2016, Volume 36, Issue 4, pp. 1813 - 1845

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 07/2015, Volume 25, Issue 8, pp. 1447 - 1476

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence,...

existence | multiplicity | nonexistence | Fractional Laplacian | Choquard equation | BOSON STARS | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | NONLINEARITIES | UNIQUENESS | LAPLACIAN | WAVES | DYNAMICS

existence | multiplicity | nonexistence | Fractional Laplacian | Choquard equation | BOSON STARS | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | NONLINEARITIES | UNIQUENESS | LAPLACIAN | WAVES | DYNAMICS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 02/2020, Volume 191, p. 111635

We consider a nonlinear pseudo-differential equation driven by the fractional p-Laplacian (−Δ)ps with s∈(0,1) and p⩾2 (degenerate case), under Dirichlet type...

Fractional [formula omitted]-Laplacian | Weighted Hölder regularity | Boundary regularity | Fractional Sobolev spaces | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | OPERATOR | REGULARITY | CONCAVE | Fractional p-Laplacian | DIRICHLET PROBLEM | Weighted Holder regularity | Sobolev space | Dirichlet problem | Differential equations

Fractional [formula omitted]-Laplacian | Weighted Hölder regularity | Boundary regularity | Fractional Sobolev spaces | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | OPERATOR | REGULARITY | CONCAVE | Fractional p-Laplacian | DIRICHLET PROBLEM | Weighted Holder regularity | Sobolev space | Dirichlet problem | Differential equations

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 10/2017, Volume 162, p. 1

We prove that a nonlocal functional approximating the standard Dirichlet p-norm fails to decrease under two-point rearrangement. Furthermore, we get other...

Nonlinear equations | Functionals | Dirichlet problem | Mathematical functions | Nonlinear systems

Nonlinear equations | Functionals | Dirichlet problem | Mathematical functions | Nonlinear systems

Journal Article

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 06/2014, Volume 414, Issue 1, pp. 372 - 385

By exploiting a suitable Trudinger-Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of...

MATHEMATICS | MATHEMATICS, APPLIED | Trudinger-Moser inequality | SPACES | INEQUALITY | EQUATIONS | Nonlocal equations | TRUDINGER | Fractional Laplacian

MATHEMATICS | MATHEMATICS, APPLIED | Trudinger-Moser inequality | SPACES | INEQUALITY | EQUATIONS | Nonlocal equations | TRUDINGER | Fractional Laplacian

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 1, pp. 844 - 859

We investigate the stability of ground states to a nonlinear focusing Schrödinger equation in presence of a Kirchhoff term. Through a spectral analysis of the...

Ground state | Modulation stability | Kirchhoff equations

Ground state | Modulation stability | Kirchhoff equations

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2012, Volume 393, Issue 2, pp. 692 - 696

We obtain the existence and uniqueness, regularity and boundary behavior for a class of singular quasi-linear elliptic equations in a smooth bounded domain.

Singular elliptic equations | Qualitative behavior | Quasi-linear elliptic equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED

Singular elliptic equations | Qualitative behavior | Quasi-linear elliptic equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 12/2016, Volume 195, Issue 6, pp. 1917 - 1959

We study an eigenvalue problem in the framework of double phase variational integrals, and we introduce a sequence of nonlinear eigenvalues by a minimax...

Double phase problems | Quasilinear problems | Gamma $$ Γ -convergence | 35J92 | Stability of eigenvalues | Mathematics, general | Musielak–Orlicz spaces | Mathematics | 47A75 | 35P30 | Weyl-type laws | Nonstandard growth conditions | Γ -convergence | EXISTENCE | MATHEMATICS, APPLIED | STABILITY | GRADIENT | MINIMIZERS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | P-LAPLACIAN | CONTINUITY | Musielak-Orlicz spaces | REGULARITY | Gamma-convergence | ELLIPTIC-EQUATIONS | FUNCTIONALS | Convergence (Social sciences)

Double phase problems | Quasilinear problems | Gamma $$ Γ -convergence | 35J92 | Stability of eigenvalues | Mathematics, general | Musielak–Orlicz spaces | Mathematics | 47A75 | 35P30 | Weyl-type laws | Nonstandard growth conditions | Γ -convergence | EXISTENCE | MATHEMATICS, APPLIED | STABILITY | GRADIENT | MINIMIZERS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | P-LAPLACIAN | CONTINUITY | Musielak-Orlicz spaces | REGULARITY | Gamma-convergence | ELLIPTIC-EQUATIONS | FUNCTIONALS | Convergence (Social sciences)

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2014, Volume 417, Issue 1, pp. 180 - 199

We investigate the soliton dynamics for a class of nonlinear Schrödinger equations with a non-local nonlinear term. In particular, we consider what we call...

Hartree equation | Modulational stability | Soliton dynamics | Ground states | Choquard equation | SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | STABILITY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | TIME | UNIQUENESS | MATHEMATICS | GROUND-STATES | SEMICLASSICAL LIMIT

Hartree equation | Modulational stability | Soliton dynamics | Ground states | Choquard equation | SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | STABILITY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | TIME | UNIQUENESS | MATHEMATICS | GROUND-STATES | SEMICLASSICAL LIMIT

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2016, Volume 55, Issue 2, pp. 1 - 32

We obtain the sharp asymptotic behavior at infinity of extremal functions for the fractional critical Sobolev embedding.

49K22 | 46E35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 35B40 | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | SPACES | EQUATIONS | BREZIS | Infinity | Partial differential equations | Asymptotic properties | Mathematical analysis | Inequalities | Decay | Calculus of variations | Optimization | Functional Analysis | Analysis of PDEs

49K22 | 46E35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 35B40 | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | SPACES | EQUATIONS | BREZIS | Infinity | Partial differential equations | Asymptotic properties | Mathematical analysis | Inequalities | Decay | Calculus of variations | Optimization | Functional Analysis | Analysis of PDEs

Journal Article

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