Journal of Differential Equations, ISSN 0022-0396, 09/2018, Volume 265, Issue 6, pp. 2648 - 2670

In this paper we study the existence of weak solutions to initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary...

Non-cylindrical domain | Parabolic equation | Mixed boundary condition | Existence

Non-cylindrical domain | Parabolic equation | Mixed boundary condition | Existence

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 06/2018, Volume 38, Issue 6, pp. 3023 - 3032

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2019, Volume 58, Issue 2, pp. 1 - 17

In this paper we consider steady vortex solutions for the ideal incompressible Euler equation in a planar bounded domain. By solving a variational problem for...

Secondary 35B35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 76B47 | Primary 76B03 | Mathematics | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | RINGS | REARRANGEMENTS | POINTS | CONFIGURATIONS | FLOW | PAIRS | Information science | Force and energy | Resveratrol

Secondary 35B35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 76B47 | Primary 76B03 | Mathematics | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | RINGS | REARRANGEMENTS | POINTS | CONFIGURATIONS | FLOW | PAIRS | Information science | Force and energy | Resveratrol

Journal Article

4.
Full Text
Multiplicity of positive and nodal solutions for nonlinear elliptic problems in a".sup.N

Annales de l'Institut Henri Poincare / Analyse non lineaire, ISSN 0294-1449, 09/2016, Volume 13, Issue 5, p. 567

We are concerned with the multiplicity of positive and nodal solutions of {-[DELTA]u+[mu]u=Q(x)|u|.sup.p-2uina.sup.Nu[member of]H.sup.1(a.sup.N) where...

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2018, Volume 197, Issue 4, pp. 1227 - 1246

This paper deals with the following supercritical Hénon-type equation $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=|x|^\alpha |u|^{p_\alpha...

35J40 | Secondary 35J05 | Lyapunov–Schmidt reduction | Hénon-type equation | Mathematics, general | Mathematics | Primary 35J60 | Sign-changing bubble tower solutions | Information science

35J40 | Secondary 35J05 | Lyapunov–Schmidt reduction | Hénon-type equation | Mathematics, general | Mathematics | Primary 35J60 | Sign-changing bubble tower solutions | Information science

Journal Article

Journal of Mathematical Sciences (Japan), ISSN 1340-5705, 2017, Volume 24, Issue 2, pp. 159 - 194

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 12/2013, Volume 54, Issue 12, p. 121511

In this paper, we are concerned with the Cauchy problem of the inhomogeneous Hartree equation: \documentclass[12pt]{minimal}\begin{document}$iu_{t}= -\Delta u...

NONLINEAR SCHRODINGER-EQUATIONS | PHYSICS, MATHEMATICAL | GLOBAL WELL-POSEDNESS | SCATTERING | Critical point | Cauchy problem | Mathematical analysis | EQUATIONS | MATHEMATICAL SOLUTIONS | CAUCHY PROBLEM | MATHEMATICAL METHODS AND COMPUTING | MASS

NONLINEAR SCHRODINGER-EQUATIONS | PHYSICS, MATHEMATICAL | GLOBAL WELL-POSEDNESS | SCATTERING | Critical point | Cauchy problem | Mathematical analysis | EQUATIONS | MATHEMATICAL SOLUTIONS | CAUCHY PROBLEM | MATHEMATICAL METHODS AND COMPUTING | MASS

Journal Article

8.
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Solutions for semilinear elliptic equations with critical exponents and Hardy potential

Journal of Differential Equations, ISSN 0022-0396, 2004, Volume 205, Issue 2, pp. 521 - 537

In this paper, we answer affirmatively an open problem (cf. Theorem 4′ in Ferrero and Gazzola (J. Differential Equations 177 (2001) 494): Let Ω∋0 be an...

Energy functional | Palais–Smale condition | Critical Sobolev exponent | Semilinear elliptic equation | Palais-Smale condition | EXISTENCE | MATHEMATICS | semilinear elliptic equation | INEQUALITIES | energy functional | critical Sobolev exponent | CRITICAL SOBOLEV

Energy functional | Palais–Smale condition | Critical Sobolev exponent | Semilinear elliptic equation | Palais-Smale condition | EXISTENCE | MATHEMATICS | semilinear elliptic equation | INEQUALITIES | energy functional | critical Sobolev exponent | CRITICAL SOBOLEV

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2019, Volume 147, Issue 2, pp. 775 - 784

In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar...

STEADY | MATHEMATICS | MATHEMATICS, APPLIED | REARRANGEMENTS | CONFIGURATIONS | FLOW

STEADY | MATHEMATICS | MATHEMATICS, APPLIED | REARRANGEMENTS | CONFIGURATIONS | FLOW

Journal Article

Science China Mathematics, ISSN 1674-7283, 2019

SCIENCE CHINA Mathematics,2019 In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization...

Euler equation | variational problem | 35Q35 | 76B03 | 76B47 | irrotational flow | incompressible fluids | vortex patch | Mathematics - Analysis of PDEs

Euler equation | variational problem | 35Q35 | 76B03 | 76B47 | irrotational flow | incompressible fluids | vortex patch | Mathematics - Analysis of PDEs

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2018, Volume 57, Issue 2, pp. 1 - 19

In this paper, we are concerned with the following nonlinear supercritical elliptic problem with variable exponent, $$\begin{aligned} {\left\{...

Secondary 35B45 | 47J30 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Primary 35B40 | Mathematics | EXISTENCE | MATHEMATICS | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS, APPLIED | LINEAR ELLIPTIC-EQUATIONS | Information science

Secondary 35B45 | 47J30 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Primary 35B40 | Mathematics | EXISTENCE | MATHEMATICS | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS, APPLIED | LINEAR ELLIPTIC-EQUATIONS | Information science

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 4/2014, Volume 212, Issue 1, pp. 179 - 217

In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation....

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CIRCULATION | IDEAL FLUID | RINGS | PLASMA PROBLEM | FLOWS | REARRANGEMENTS | SYMMETRIC VORTEX PAIRS | CONFIGURATIONS | Construction | Approximation | Mathematical analysis | Vortices | Fluid flow | Texts | Euler equations | Regularization

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CIRCULATION | IDEAL FLUID | RINGS | PLASMA PROBLEM | FLOWS | REARRANGEMENTS | SYMMETRIC VORTEX PAIRS | CONFIGURATIONS | Construction | Approximation | Mathematical analysis | Vortices | Fluid flow | Texts | Euler equations | Regularization

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 07/2010, Volume 38, Issue 3, pp. 471 - 501

In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth and a Hardy potential:...

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | GLOBAL COMPACTNESS RESULT | CRITICAL NONLINEARITIES | HEAT-EQUATION | INEQUALITY | BOUNDARY-VALUE-PROBLEMS | CRITICAL EXPONENTS | Partial differential equations | Mathematical analysis | Calculus of variations

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | GLOBAL COMPACTNESS RESULT | CRITICAL NONLINEARITIES | HEAT-EQUATION | INEQUALITY | BOUNDARY-VALUE-PROBLEMS | CRITICAL EXPONENTS | Partial differential equations | Mathematical analysis | Calculus of variations

Journal Article

Journal of Mathematical Sciences (Japan), ISSN 1340-5705, 2015, Volume 22, Issue 2, pp. 531 - 568

Journal Article

Nonlinearity, ISSN 0951-7715, 04/2019, Volume 32, Issue 5, pp. 1882 - 1904

The vortex-wave system describes the motion of a two-dimensional ideal fluid in which the vorticity includes continuously distributed vorticity, which is...

maximization | Euler equation | desingularization | vortex-wave system | vortex patch | Kirchhoff-Routh function | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

maximization | Euler equation | desingularization | vortex-wave system | vortex patch | Kirchhoff-Routh function | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2015, Volume 113, pp. 94 - 114

In this paper we are concerned with the stationary and non-stationary Stokes and Navier–Stokes problems with mixed boundary conditions involving velocity,...

Navier–Stokes equations | Stress boundary condition | Uniqueness | Rotation boundary condition | Mixed boundary condition | Pressure boundary condition | Existence | Navier-Stokes equations | VANISHING VISCOSITY LIMIT | MATHEMATICS, APPLIED | SOLVABILITY | EQUATIONS | VARIATIONAL INEQUALITY | FLOW | MATHEMATICS | PRESSURE | REGULARITY | FINITE-ELEMENT-METHOD | Fluid dynamics | Computational fluid dynamics | Fluid flow | Boundary conditions | Derivatives | Fields (mathematics) | Boundaries | Stokes law (fluid mechanics)

Navier–Stokes equations | Stress boundary condition | Uniqueness | Rotation boundary condition | Mixed boundary condition | Pressure boundary condition | Existence | Navier-Stokes equations | VANISHING VISCOSITY LIMIT | MATHEMATICS, APPLIED | SOLVABILITY | EQUATIONS | VARIATIONAL INEQUALITY | FLOW | MATHEMATICS | PRESSURE | REGULARITY | FINITE-ELEMENT-METHOD | Fluid dynamics | Computational fluid dynamics | Fluid flow | Boundary conditions | Derivatives | Fields (mathematics) | Boundaries | Stokes law (fluid mechanics)

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 08/2015, Volume 259, Issue 3, pp. 838 - 872

In this paper, we present a new scheme to study the dynamics of a stochastic reaction–diffusion equation with the nonlinearity satisfying a dissipative...

Continuity in [formula omitted] | Stochastic reaction–diffusion equation | [formula omitted]-attraction | Higher-order integrability | Continuity in H01(Q) | (L 2 (Q), L 2+δ (Q))-attraction | Stochastic reaction-diffusion equation | EXISTENCE | RANDOM ATTRACTORS | Continuity in H-0(Q) | H-1-RANDOM ATTRACTORS | (L-2(Q), L2+delta(Q))-attraction | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | PULLBACK ATTRACTORS | DIMENSION | RANDOM INVARIANT SET | SYSTEMS | UNBOUNDED-DOMAINS

Continuity in [formula omitted] | Stochastic reaction–diffusion equation | [formula omitted]-attraction | Higher-order integrability | Continuity in H01(Q) | (L 2 (Q), L 2+δ (Q))-attraction | Stochastic reaction-diffusion equation | EXISTENCE | RANDOM ATTRACTORS | Continuity in H-0(Q) | H-1-RANDOM ATTRACTORS | (L-2(Q), L2+delta(Q))-attraction | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | PULLBACK ATTRACTORS | DIMENSION | RANDOM INVARIANT SET | SYSTEMS | UNBOUNDED-DOMAINS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 10/2013, Volume 255, Issue 7, pp. 2018 - 2064

We consider the Cauchy problem for the nonlinear Schrödinger equation i∂tu+Δu=λ0u+λ1|u|αu in RN, where λ0,λ1∈C, in Hs subcritical and critical case: 0<α⩽4N−2s...

Continuous dependence | Nonlinear Schrödinger equation | Cauchy problem

Continuous dependence | Nonlinear Schrödinger equation | Cauchy problem

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 04/2010, Volume 51, Issue 4

In this paper, we study the Cauchy problem of the inhomogeneous nonlinear Schroedinger equation with a harmonic potential: i{partial_derivative}{sub...

HARMONIC POTENTIAL | MATHEMATICAL SOLUTIONS | NONLINEAR PROBLEMS | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CRITICAL MASS | CAUCHY PROBLEM | BOSE-EINSTEIN CONDENSATION

HARMONIC POTENTIAL | MATHEMATICAL SOLUTIONS | NONLINEAR PROBLEMS | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CRITICAL MASS | CAUCHY PROBLEM | BOSE-EINSTEIN CONDENSATION

Journal Article

20.
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Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 12/2015, Volume 54, Issue 4, pp. 4037 - 4063

We are concerned with the following nonlinear Schrödinger equation $$\begin{aligned} -\varepsilon ^2\Delta u+ V(x)u=|u|^{p-2}u,\quad u\in H^1(\mathbb {R}^N),...

35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35J60 | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | EXISTENCE | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | PEAKS | SEMICLASSICAL STATES | EXPONENT | ELLIPTIC-EQUATIONS | POTENTIALS

35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35J60 | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | EXISTENCE | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | PEAKS | SEMICLASSICAL STATES | EXPONENT | ELLIPTIC-EQUATIONS | POTENTIALS

Journal Article

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