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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
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
Journal Article
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
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
Journal Article
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
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
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
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2018, Volume 57, Issue 2, pp. 1 - 19
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 4/2014, Volume 212, Issue 1, pp. 179 - 217
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
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
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 08/2015, Volume 259, Issue 3, pp. 838 - 872
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
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
Journal Article
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
Journal Article
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