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Nonlinear Analysis, ISSN 0362-546X, 01/2020, Volume 190, p. 111604
Consider the nonlinear scalar field equation (0.1)−Δu=f(u)inRN,u∈H1(RN),where N≥3 and f satisfies the general Berestycki–Lions conditions. We are interested in... 
Nonradial solutions | Monotonicity trick | Nonlinear scalar field equations | Berestycki–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 | Onsager’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 Schrödinger equations −△u+V(x)u=g(u),x∈RN, N≥3, where g satisfies Berestycki–Lions conditions and V is a small... 
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
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 02/2018, Volume 365, pp. 12 - 26
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
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
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 Friedmann–Lemaître–Robertson–Walker (FLRW) flat... 
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
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 ≥ 2,... 
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 Klein–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
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
Journal Article
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
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
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 - Δ ) α 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
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
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
Journal Article