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Communications in Contemporary Mathematics, ISSN 0219-1997, 2017, Volume 20, Issue 3, p. 1750017
In this paper, we study the existence of positive multi-peak solutions to the fractional Schrodinger-Poisson system {is an element of 2s (-Delta)(s)u + V(x)u +... 
variational methods | multi-peak solutions | Fractional Schrödinger–Poisson system | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | WAVES | GROUND-STATE | MAXWELL EQUATIONS | Fractional Schrodinger-Poisson system
Journal Article
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, ISSN 0308-2105, 08/2019, Volume 149, Issue 4, pp. 1097 - 1122
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 12/2018, Volume 57, Issue 6, pp. 1 - 28
Journal Article
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, ISSN 0253-4142, 04/2018, Volume 128, Issue 2, p. 1
We consider the existence of single and multi-peak solutions of the following nonlinear elliptic Neumann problem {-Delta u +lambda(2)u = Q(x)vertical bar u... 
Elliptic equation | nonlinear boundary condition | singular perturbation | multi-peak solutions | EXISTENCE | MATHEMATICS | R-N | NODAL SOLUTIONS | MULTIPLICITY | R-+(N) | NEUMANN PROBLEM | UNIQUENESS | Research | Functions, Elliptic | Mathematical research | Perturbation (Mathematics)
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2014, Volume 409, Issue 2, pp. 684 - 704
In this paper, we are concerned with the following two coupled Schrödinger systems in a bounded domain Ω⊂RN(N=2,3) with Neumann boundary conditions... 
Neumann boundary condition | Variational methods | Multi-peak solutions | Coupled Schrödinger systems | MATHEMATICS | MATHEMATICS, APPLIED | R-N | STATES | WAVES | POSITIVE SOLUTIONS | SPIKES | EQUATIONS | Coupled Schrodinger systems
Journal Article
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, ISSN 0025-5645, 07/2013, Volume 65, Issue 3, pp. 887 - 929
In this paper, we study the existence and the asymptotic behavior of a positive solution to the one-dimensional stationary shadow system of the... 
Gierer-Meinhardt system | transition layer | STABILITY | SPIKES | STABLE-SOLUTIONS | NEUMANN PROBLEM | MATHEMATICS | PATTERN-FORMATION | INTERNAL LAYERS | Liapunov-Schmidt | REACTION-DIFFUSION SYSTEMS | SEMILINEAR ELLIPTIC SYSTEM | LEAST-ENERGY SOLUTIONS | saturation effect | MULTI-PEAK SOLUTIONS
Journal Article
ADVANCED NONLINEAR STUDIES, ISSN 1536-1365, 02/2020, Volume 20, Issue 1, pp. 53 - 75
In this paper, we study the following nonlinear Schrodinger-Newton type system: {-epsilon(2)Delta u + u - Phi(x)u = Q(x)vertical bar u vertical bar u, x... 
EXISTENCE | HARTREE | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | SPHERES | EQUATIONS | MOLECULES | Local minimum | MATHEMATICS | BOUND-STATES | SOLITARY WAVES | POISSON PROBLEM | Schrodinger-Newton Type System | ATOMS | Multi-peak Solutions
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 11/2014, Volume 14, Issue 4, pp. 951 - 975
In this paper, we study a nonlinear Schrodinger equation with magnetic fields involving subcritical growth. Applying the finite reduction method, we prove that... 
Magnetic fields | Multi-peak solutions | Nonlinear Schrödinger equation | EXISTENCE | MATHEMATICS, APPLIED | Nonlinear Schrodinger equation | POSITIVE SOLUTIONS | BUMP SOLUTIONS | ELECTROMAGNETIC-FIELDS | UNIQUENESS | SEMICLASSICAL BOUND-STATES | MATHEMATICS | ELLIPTIC PROBLEMS | NLS EQUATIONS | DOMAIN TOPOLOGY | CRITICAL SOBOLEV EXPONENT
Journal Article
by Li, GB and Niu, YH
ACTA MATHEMATICA SCIENTIA, ISSN 0252-9602, 01/2020, Volume 40, Issue 1, pp. 90 - 112
In the present paper, we consider the nonlocal Kirchhoff problem, where a, b < 0, 1 > p > 5} and < 0 is a parameter. Under some assumptions on Q(x), we show... 
SCHRODINGER-EQUATIONS | MATHEMATICS | local uniqueness | MULTIPLICITY | BOUND-STATES | Lyapunov-Schmidt reduction | local Pohozaev identity | R-3 | multi-peak positive solutions | Kirchhoff equations
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 1, pp. 641 - 656
In this paper we prove some symmetry results for positive solutions of the semilinear elliptic equations of the type Δu+f(u)=0 with mixed boundary conditions... 
Monotonicity | Symmetry | Moving plane method | MATHEMATICS | MATHEMATICS, APPLIED | SINGULAR PERTURBATION PROBLEMS | MAXIMUM PRINCIPLE | LEAST-ENERGY SOLUTIONS | SEMILINEAR NEUMANN PROBLEM | LAYER SOLUTIONS | DOMAINS | MULTI-PEAK SOLUTIONS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 352, Issue 1, pp. 246 - 258
We study the existence, multiplicity and shape of positive solutions of the system − ε 2 Δ u + V ( x ) u = K ( x ) g ( v ) , − ε 2 Δ v + V ( x ) v = H ( x ) f... 
Singular perturbations | Superlinear elliptic systems | Spike-layered solutions | Minimax methods | EXISTENCE | LOCATION | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | SEMICLASSICAL STATES | MATHEMATICS | SHAPE | POSITIVE BOUND-STATES | LEAST-ENERGY SOLUTIONS | MULTI-PEAK SOLUTIONS | Analysis | Universities and colleges
Journal Article
by Hu, TX and Shuai, W
JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, 10/2018, Volume 265, Issue 8, pp. 3587 - 3617
We are concerned with the existence of multi-peak solutions to Kirchhoff equation -(epsilon(2)a + epsilon b integral(R)3 vertical bar del u vertical bar(2)dx)... 
SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS | Multi-peak solution | Kirchhoff equation | BOUND-STATES | POSITIVE SOLUTIONS | BEHAVIOR | Variational method
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 07/2015, Volume 35, Issue 7, pp. 3183 - 3201
In this paper we study the existence of positive multi-peak solutions to the semilinear equation epsilon(2s) (-Delta)(s) u + u = Q (x)u(p) (1), u > 0, u is an... 
Fractional elliptic equation | Critical point | Lyapunov-Schmidt reduction | Multi-peak solutions | LAPLACIAN | MATHEMATICS | critical point | MATHEMATICS, APPLIED | multi-peak solutions | SCHRODINGER-EQUATION | UNIQUENESS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2017, Volume 263, Issue 11, pp. 7221 - 7249
We consider the following slightly subcritical problem(℘ε){−Δu=β(x)|u|p−1−εuin Ω,u=0on ∂Ω, where Ω is a smooth bounded domain in Rn, 3≤n≤6, p:=n+2n−2 is the... 
Blowing up solutions | Critical exponent | Hénon problem | MATHEMATICS | ELLIPTIC PROBLEMS | NODAL SOLUTIONS | PROFILE | GROWTH | Henon problem | EQUATION | MULTI-PEAK SOLUTIONS | CRITICAL-POINTS
Journal Article
by Li, GB and Niu, YH and Xiang, CL
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, ISSN 1239-629X, 2020, Volume 45, Issue 1, pp. 121 - 137
In this paper, we consider the nonlocal Kirchhoff problem -(c(2)a + cb integral(R3 )vertical bar del u vertical bar(2)) Delta u + V(x)u = u(p), u > 0, u is an... 
EXISTENCE | local uniqueness | NONLINEAR SCHRODINGER-EQUATIONS | MULTIPLICITY | local Pohozaev identity | POSITIVE SOLUTIONS | BUMP | multi-peak positive solutions | Kirchhoff equations | MATHEMATICS | BOUND-STATES | R-3 | CONCENTRATION BEHAVIOR
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 05/2016, Volume 16, Issue 2, pp. 231 - 247
Journal Article
Annales de l'Institut Henri Poincare / Analyse non lineaire, ISSN 0294-1449, 2010, Volume 27, Issue 5, pp. 1205 - 1226
In this paper, we will study the existence and qualitative property of standing waves ψ ( x , t ) = e − i E t ε u ( x ) for the nonlinear Schrödinger equation... 
Nonlinear Schrödinger equation | Bound state | Multi-peak solutions | Potentials compactly supported or unbounded at infinity | EXISTENCE | INFINITY | MATHEMATICS, APPLIED | Nonlinear Schrodinger equation | POSITIVE SOLUTIONS | BUMP STANDING WAVES | SEMICLASSICAL STATES | CRITICAL FREQUENCY | UNIQUENESS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 07/2014, Volume 257, Issue 1, pp. 207 - 230
This paper is concerned with the existence of segregated vector solutions for{−ε2Δui+Pi(x)ui=βiui3+∑j≠inβijuiuj2,x∈Ω,ui>0,x∈Ω,i=1,…,n, where Ω is a bounded or... 
Multi-peak solutions | Reduction method | Nonlinear Schrödinger system | PHASE-SEPARATION | MATHEMATICS | LINEARLY COUPLED SYSTEMS | NONLINEAR SCHRODINGER-EQUATIONS | SOLITONS | BOUND-STATES | SOLITARY WAVES | SPIKES | Nonlinear Schrodinger system | GROUND-STATES
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 07/2015, Volume 35, Issue 7, pp. 2921 - 2948
Journal Article
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