Nonlinear Analysis, ISSN 0362-546X, 01/2020, Volume 190, p. 111604

Consider the nonlinear scalar field equation (0.1)âˆ’Î”u=f(u)inRN,uâˆˆH1(RN),where Nâ‰¥3 and f satisfies the general Berestyckiâ€“Lions conditions. We are interested in...

Nonradial solutions | Monotonicity trick | Nonlinear scalar field equations | Berestyckiâ€“Lions nonlinearity | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | KIRCHHOFF-TYPE EQUATION | SCHRODINGER-EQUATION | STANDING WAVES | Berestycki-Lions nonlinearity | MOUNTAIN-PASS | Mountains | Nonlinearity | Nonlinear equations | Critical point

Nonradial solutions | Monotonicity trick | Nonlinear scalar field equations | Berestyckiâ€“Lions nonlinearity | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | KIRCHHOFF-TYPE EQUATION | SCHRODINGER-EQUATION | STANDING WAVES | Berestycki-Lions nonlinearity | MOUNTAIN-PASS | Mountains | Nonlinearity | Nonlinear equations | Critical point

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 02/2019, Volume 179, pp. 254 - 269

We consider transport equations with an incompressible transporting vector field. Whereas smooth solutions of such equations conserve every Lp norm simply by...

Active scalar equation | Onsagerâ€™s conjecture | Renormalization | Onsager's conjecture | DISSIPATION | NONUNIQUENESS | MATHEMATICS, APPLIED | INCOMPRESSIBLE EULER | ENERGY-CONSERVATION | ONSAGERS CONJECTURE | UNIQUENESS | MATHEMATICS | SETS | WEAK SOLUTIONS | Nonlinear equations | Algebra | Mathematical analysis | Norms | Mathematical models | Fields (mathematics) | Regularity

Active scalar equation | Onsagerâ€™s conjecture | Renormalization | Onsager's conjecture | DISSIPATION | NONUNIQUENESS | MATHEMATICS, APPLIED | INCOMPRESSIBLE EULER | ENERGY-CONSERVATION | ONSAGERS CONJECTURE | UNIQUENESS | MATHEMATICS | SETS | WEAK SOLUTIONS | Nonlinear equations | Algebra | Mathematical analysis | Norms | Mathematical models | Fields (mathematics) | Regularity

Journal Article

Nonlinear Analysis. Real World Applications, ISSN 1468-1218, 02/2019, Volume 45, p. 531

In the paper, we consider the following SchrÃ¶dinger equations âˆ’â–³u+V(x)u=g(u),xâˆˆRN, Nâ‰¥3, where g satisfies Berestyckiâ€“Lions conditions and V is a small...

Mathematical problems | Nonlinear equations | Schrodinger equation | Variational methods | Mathematical analysis | Schroedinger equation | Perturbation

Mathematical problems | Nonlinear equations | Schrodinger equation | Variational methods | Mathematical analysis | Schroedinger equation | Perturbation

Journal Article

NONLINEARITY, ISSN 0951-7715, 12/2019, Volume 32, Issue 12, pp. 4942 - 4966

We study the following nonlinear scalar field equation {-Delta u -f(u) - mu u in R-N, parallel to u parallel to(2)(L2(RN)) = m, u is an element of H-1(R-N)....

SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | L-2-subcritical case | nonradial solutions | STABILITY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | STANDING WAVES | PHYSICS, MATHEMATICAL | nonlinear scalar field equations | SYMMETRY | sign-changing solutions | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | L-2-subcritical case | nonradial solutions | STABILITY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | STANDING WAVES | PHYSICS, MATHEMATICAL | nonlinear scalar field equations | SYMMETRY | sign-changing solutions | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 02/2018, Volume 365, pp. 12 - 26

In this paper we examine the scattering processes among the members of a rich family of kinks which arise in a (1+1)-dimensional relativistic two scalar field...

Two coupled scalar field theory model | Non-linear Kleinâ€“Gordon equation | Kink dynamics | Bounce resonant windows | MATHEMATICS, APPLIED | ANTIKINK INTERACTIONS | DEFECTS | PHYSICS, MULTIDISCIPLINARY | Non-linear Klein-Gordon equation | DOMAIN-WALLS | FRACTAL STRUCTURE | PHYSICS, MATHEMATICAL | COLLISIONS | SINE-GORDON KINKS | SOLITONS | RESONANCE | MODELS | EQUATION | Physics - High Energy Physics - Theory

Two coupled scalar field theory model | Non-linear Kleinâ€“Gordon equation | Kink dynamics | Bounce resonant windows | MATHEMATICS, APPLIED | ANTIKINK INTERACTIONS | DEFECTS | PHYSICS, MULTIDISCIPLINARY | Non-linear Klein-Gordon equation | DOMAIN-WALLS | FRACTAL STRUCTURE | PHYSICS, MATHEMATICAL | COLLISIONS | SINE-GORDON KINKS | SOLITONS | RESONANCE | MODELS | EQUATION | Physics - High Energy Physics - Theory

Journal Article

09/2018, 1st ed. 2019, ISBN 3319910221, 580

This book discusses innovations in the field of Directed Energy (DE) and presents new technologies and innovative approaches for use in energy production for...

Wave equation | Electromagnetic waves | Scalar field theory | Energy | Microwaves, RF and Optical Engineering | Energy, general | Microwaves

Wave equation | Electromagnetic waves | Scalar field theory | Energy | Microwaves, RF and Optical Engineering | Energy, general | Microwaves

eBook

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 1/2019, Volume 231, Issue 1, pp. 45 - 61

In this note, we uncover a relation between power-law nonlinear scalar field equations and logarithmic-law scalar field equations.We show that the ground state...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | WAVES | MECHANICS | GROUND-STATES | UNIQUENESS | Nonlinear equations | Mathematical analysis | Liouville theorem | Expanding universe theory | Ground state | Nonlinearity | Power law | Convergence

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | WAVES | MECHANICS | GROUND-STATES | UNIQUENESS | Nonlinear equations | Mathematical analysis | Liouville theorem | Expanding universe theory | Ground state | Nonlinearity | Power law | Convergence

Journal Article

International Journal of Modern Physics D, ISSN 0218-2718, 11/2019, Volume 28, Issue 15, p. 1950173

This paper deals with a nonminimally coupled scalar field in the background of homogeneous and isotropic Friedmannâ€“LemaÃ®treâ€“Robertsonâ€“Walker (FLRW) flat...

nonhyperbolic point | Friedmann-Lemaitre-Robertson-Walker flat spacetime | bifurcation | Nonminimally coupled scalar field | ASTRONOMY & ASTROPHYSICS | center manifold

nonhyperbolic point | Friedmann-Lemaitre-Robertson-Walker flat spacetime | bifurcation | Nonminimally coupled scalar field | ASTRONOMY & ASTROPHYSICS | center manifold

Journal Article

2018, Series in applied and computational mathematics, ISBN 9789813230859, Volume 3, xi, 174 pages

Book

Journal of Differential Equations, ISSN 0022-0396, 2011, Volume 251, Issue 12, pp. 3625 - 3657

We are concerned with the existence and non-existence of nontrivial weak solutions for a class of quasilinear scalar field equations in R N driven by competing...

Unbounded or decaying potentials | Fibering method | p-Laplacian | Ground states | Bound states | Weighted Sobolev spaces | P-Laplacian | Weighted sobolev spaces | NONLINEAR SCHRODINGER-EQUATIONS | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | CONCENTRATION-COMPACTNESS PRINCIPLE | DECAYING RADIAL POTENTIALS | STANDING WAVES | CRITICAL FREQUENCY | SEMICLASSICAL BOUND-STATES | MATHEMATICS | UNBOUNDED-DOMAINS | GROUND-STATES

Unbounded or decaying potentials | Fibering method | p-Laplacian | Ground states | Bound states | Weighted Sobolev spaces | P-Laplacian | Weighted sobolev spaces | NONLINEAR SCHRODINGER-EQUATIONS | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | CONCENTRATION-COMPACTNESS PRINCIPLE | DECAYING RADIAL POTENTIALS | STANDING WAVES | CRITICAL FREQUENCY | SEMICLASSICAL BOUND-STATES | MATHEMATICS | UNBOUNDED-DOMAINS | GROUND-STATES

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 03/2013, Volume 66, Issue 3, pp. 372 - 413

In this paper the equation $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}} - \Delta u + a(x)u = |u|^{p - 1} u\;{\rm in }\;{\R}^N $ is considered, when N â‰¥ 2,...

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | R-N | NONLINEAR SCHRODINGER-EQUATIONS | BOUND-STATES | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | DOMAINS

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | R-N | NONLINEAR SCHRODINGER-EQUATIONS | BOUND-STATES | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | DOMAINS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2012, Volume 396, Issue 1, pp. 323 - 344

In this article we prove the global existence of the small data solutions of the Cauchy problem for the semilinear Kleinâ€“Gordon equation in the de Sitter...

de Sitter spacetime | [formula omitted] estimates | Global solution | Higgs boson equation | De Sitter spacetime | Lp-Lq estimates | L-p - L-q estimates | MATHEMATICS | MATHEMATICS, APPLIED | KLEIN-GORDON EQUATION | MASS | Higgs boson equations | NONLINEAR-WAVE EQUATIONS

de Sitter spacetime | [formula omitted] estimates | Global solution | Higgs boson equation | De Sitter spacetime | Lp-Lq estimates | L-p - L-q estimates | MATHEMATICS | MATHEMATICS, APPLIED | KLEIN-GORDON EQUATION | MASS | Higgs boson equations | NONLINEAR-WAVE EQUATIONS

Journal Article

Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, ISSN 1120-6330, 2015, Volume 26, Issue 1, pp. 75 - 82

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 5/2015, Volume 53, Issue 1, pp. 29 - 64

We prove the stability of the Einstein-scalar field Lichnerowicz equation under subcritical perturbations of the critical nonlinearity in dimensions $$n = 3,...

83C05 | 58J99 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | COMPACT RIEMANNIAN-MANIFOLDS | CONSTRAINT EQUATIONS | MEAN-CURVATURE | Cosmological constant | Stability | Perturbation methods | Partial differential equations | Mathematical analysis | Texts | Nonlinearity | Calculus of variations

83C05 | 58J99 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | COMPACT RIEMANNIAN-MANIFOLDS | CONSTRAINT EQUATIONS | MEAN-CURVATURE | Cosmological constant | Stability | Perturbation methods | Partial differential equations | Mathematical analysis | Texts | Nonlinearity | Calculus of variations

Journal Article

15.
Infinitely many positive and sign-changing solutions for nonlinear fractional scalar field equations

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 02/2016, Volume 36, Issue 2, pp. 917 - 939

We consider the following nonlinear fractional scalar field equation (-Delta)(s)u + u = K(vertical bar x vertical bar u(p), u > 0 in R-N, where K(vertical bar...

Nonlinear scalar field equation | Fractional Laplacian | Reduction method | EXISTENCE | MATHEMATICS | nonlinear scalar field equation | MATHEMATICS, APPLIED | WAVES | BOUND-STATES | REGULARITY | reduction method

Nonlinear scalar field equation | Fractional Laplacian | Reduction method | EXISTENCE | MATHEMATICS | nonlinear scalar field equation | MATHEMATICS, APPLIED | WAVES | BOUND-STATES | REGULARITY | reduction method

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 05/2016, Volume 33, Issue 11, p. 115010

We determine the class of p-forms F that possess vanishing scalar invariants (VSIs) at arbitrary order in an n-dimensional spacetime. Namely, we prove that F...

Einstein-maxwell spacetimes | exact solutions | higher dimensions | BACKGROUNDS | NONLINEAR ELECTRODYNAMICS | COSMOLOGICAL CONSTANT | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | 11-DIMENSIONAL SUPERGRAVITY | einstein-maxwell spacetimes | GRAVITATIONAL-WAVES | ASTRONOMY & ASTROPHYSICS | N SOLUTIONS | BORN-INFELD | SPACE-TIMES | PHYSICS, PARTICLES & FIELDS

Einstein-maxwell spacetimes | exact solutions | higher dimensions | BACKGROUNDS | NONLINEAR ELECTRODYNAMICS | COSMOLOGICAL CONSTANT | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | 11-DIMENSIONAL SUPERGRAVITY | einstein-maxwell spacetimes | GRAVITATIONAL-WAVES | ASTRONOMY & ASTROPHYSICS | N SOLUTIONS | BORN-INFELD | SPACE-TIMES | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 3/2017, Volume 19, Issue 1, pp. 649 - 690

In this paper, the existence of least energy solution and infinitely many solutions is proved for the equation $$(1-\Delta )^\alpha u = f(u)$$ ( 1 - Î” ) Î± u =...

Mathematical Methods in Physics | The Pohozaev identity | 35J60 | Analysis | Mountian pass theorem | Mathematics, general | Symmetric mountain pass theorem | Mathematics | Variational method | 35S05 | MATHEMATICS, APPLIED | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | NONLINEAR SCHRODINGER-EQUATION | LAPLACIAN | MATHEMATICS | R-N | SOBOLEV SPACES | GROUND-STATES

Mathematical Methods in Physics | The Pohozaev identity | 35J60 | Analysis | Mountian pass theorem | Mathematics, general | Symmetric mountain pass theorem | Mathematics | Variational method | 35S05 | MATHEMATICS, APPLIED | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | NONLINEAR SCHRODINGER-EQUATION | LAPLACIAN | MATHEMATICS | R-N | SOBOLEV SPACES | GROUND-STATES

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 6/2019, Volume 368, Issue 2, pp. 519 - 584

We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | CAUCHY HYPERSURFACES | SPACE | PHYSICS, MATHEMATICAL | Analysis | Kinematics

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | CAUCHY HYPERSURFACES | SPACE | PHYSICS, MATHEMATICAL | Analysis | Kinematics

Journal Article

The European Physical Journal C, ISSN 1434-6044, 6/2017, Volume 77, Issue 6, pp. 1 - 11

We derive an exact solution belonging to the Kundt class of spacetimes both with and without a cosmological constant that are minimally coupled to a free...

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | TENSOR | GENERAL-RELATIVITY | GRAVITATIONAL-WAVES | CURVATURE | ALGORITHM | CONFINEMENT | CLASSIFICATION | MODEL | PHYSICS, PARTICLES & FIELDS | Electromagnetic fields | Cosmological constant | Nonlinear equations | Spacetime | Physics - General Relativity and Quantum Cosmology | General Relativity and Quantum Cosmology | Nuclear and particle physics. Atomic energy. Radioactivity | Astrophysics

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | TENSOR | GENERAL-RELATIVITY | GRAVITATIONAL-WAVES | CURVATURE | ALGORITHM | CONFINEMENT | CLASSIFICATION | MODEL | PHYSICS, PARTICLES & FIELDS | Electromagnetic fields | Cosmological constant | Nonlinear equations | Spacetime | Physics - General Relativity and Quantum Cosmology | General Relativity and Quantum Cosmology | Nuclear and particle physics. Atomic energy. Radioactivity | Astrophysics

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 10/2017, Volume 193, Issue 1, pp. 1429 - 1443

We consider a nonlinear differential equation arising in mathematical models of elementary particle theory. For this equation, we examine questions of the...

nonlinear scalar field differential equation | solution extendibility | particle-like solution | solution bounded at infinity | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Differential equations

nonlinear scalar field differential equation | solution extendibility | particle-like solution | solution bounded at infinity | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Differential equations

Journal Article