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Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2008, Volume 360, Issue 7, pp. 3813 - 3837
In this paper we study the existence and qualitative property of standing wave solutions \psi(x,t) = e^{-\frac{iEt}{\hbar}} u(x) for the nonlinear Schrödinger... 
Standing waves | Interior points | Critical points | Inner products | Uniqueness | Maximum principle | Ground state | Mountain passes | Critical frequencies | Mathematics | Critical point | Multiscale-bump | Variational method | Nonlinear Schrödinger equation | EXISTENCE | MATHEMATICS | FIELD-EQUATIONS | SEMICLASSICAL STATES | MULTILUMP BOUND-STATES | MULTIPLE POSITIVE SOLUTIONS | UNIQUENESS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2004, Volume 203, Issue 2, pp. 292 - 312
In this paper we study the existence and qualitative property of standing wave solutions ψ(x,t)=e − iEt ℏ u(x) for the nonlinear Schrödinger equation iℏ ∂ψ ∂t... 
Standing waves | Variational method | Nonlinear Schrödinger equation | Multi-bump | EXISTENCE | MATHEMATICS | BOUND-STATES | variational method | multi-bump | nonlinear Schrodinger equation | SEMICLASSICAL STATES | standing waves
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
Quarterly of Applied Mathematics, ISSN 0033-569X, 9/2006, Volume 64, Issue 3, pp. 463 - 482
Journal Article
Advances in Differential Equations, ISSN 1079-9389, 2001, Volume 6, Issue 8, pp. 931 - 958
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 2001, Volume 1, Issue 2, pp. 43 - 77
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2000, Volume 166, Issue 2, pp. 266 - 289
This paper is concerned with the existence of multi-peak solutions of the following problem[formula] where Ω is a smooth bounded domain in RN (N⩾2), ε>0 is a... 
singular perturbation | semilinear elliptic problems | multi-peak solutions | Semilinear elliptic problems | Multi-peak solutions | Singular perturbation | EXISTENCE | INFINITY | MATHEMATICS | DOMAIN SHAPE | NUMBER | NONLINEAR EQUATIONS | SOBOLEV EXPONENT | POSITIVE SOLUTIONS | UNIQUENESS
Journal Article
Indiana University mathematics journal, ISSN 0022-2518, 1995, Volume 44, Issue 4
Journal Article
Annales de l'Institut Henri Poincare / Analyse non lineaire, ISSN 0294-1449, 1998, Volume 15, Issue 1, pp. 73 - 111
A one to one correspondence is established between the nondegenerate critical points of Q( x) in Ω and single peaked solutions of the problem −ϵ 2δu+u=Q(x)u... 
MATHEMATICS, APPLIED | DOMAIN | SHAPE | CRITICAL SOBOLEV EXPONENT | POSITIVE SOLUTIONS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/1995, Volume 195, Issue 1, pp. 278 - 293
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 11/2002, Volume 15, Issue 3, pp. 403 - 419
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 12/1997, Volume 46, Issue 4, pp. 1255 - 1271
The existence of a nodal solution with least energy is established for the problem $\underset{u \in H^{1}_{0}(\Omega)}{-\varepsilon ^{2} \Delta u + u =... 
Geometry | Local minimum | Mathematics | Local maximum | College mathematics | Mathematical notation | MATHEMATICS | SHAPE
Journal Article
Canadian journal of mathematics, ISSN 0008-414X, 10/1992, Volume 44, Issue 5, pp. 1014 - 1029
Existence theorems and asymptotic properties will be obtained for boundary value problems of the form in an unbounded domain Ω⊆ RN(N ≥3) with smooth boundary,... 
EXISTENCE | MATHEMATICS | EQUATIONS | CRITICAL SOBOLEV EXPONENTS
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 8/2000, Volume 62, Issue 1, pp. 213 - 227
In this paper we continue our investigation in [5, 7, 8] on multipeak solutions to the problem formula here where Δ = [sum ]Ni=1δ2/δx2i is the Laplace operator... 
SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS | BOUND-STATES | DOMAIN TOPOLOGY | NEUMANN PROBLEM | SINGLE-PEAKED SOLUTIONS | CRITICAL SOBOLEV EXPONENT | UNIQUENESS
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 10/1989, Volume 38, Issue 3, pp. 557 - 561
Journal Article
Discrete and Continuous Dynamical Systems, ISSN 1078-0947, 09/2004, Volume 11, Issue 2-3, pp. 649 - 666
We study the profile of solutions of -Deltau + (lambda - h(x))u = g(x)(u(p-1) + f(u)) in R-N, u > 0 in R-N, u is an element of H-1(R-N), where lambda > 0 is a... 
Profile of solutions | Nonlinear elliptic problem | Eletromagnetic guided waves | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | CALCULUS | FIELD | CONCENTRATION-COMPACTNESS PRINCIPLE | nonlinear elliptic problem | EQUATIONS | profile of solutions | eletromagnetic guided waves | UNIQUENESS
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 01/2000, Volume 25, Issue 11-12, pp. 2185 - 2232
... ELLIPTIC PROBLEMS Daomin Cao* 1nst)itute of Applied Mathematics, Chinese Academy of Scicnces Beijing 100080, P.R. China and Ezzat S. Noussairt School of h~Tathemat,ics... 
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 1979, Volume 34, Issue 3, pp. 482 - 495
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 11/2002, Volume 15, Issue 3, pp. 403 - 419
We prove the existence of two peak solutions for the scalar curvature equation $-\Delta u=(1+\varepsilon K(x))u^{(N+2)/(N-2)}$ in ${\mathbb R}^N$ , if K(x) has... 
Mathematics Subject Classification : 35J60, 35J65
Journal Article
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