On the Classification of Standing Wave Solutions for the Schrödinger Equation

DOI10.1080/03605300903419767zbMath1191.35130OpenAlexW1971291495MaRDI QIDQ3550973

Yong-Li Tang, Zhi-You Chen, Jhih-He Chen, Jann-Long Chern

Publication date: 8 April 2010

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300903419767

zbMATH Keywords

Klein-Gordon equationSchrödinger equationstanding wave solution

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear elliptic equations (35J61) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (10)

Singular extremal solutions for supercritical elliptic equations in a ball ⋮ Existence and uniqueness of singular solutions for elliptic equation on the hyperbolic space ⋮ A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth ⋮ Singular solutions for semilinear elliptic equations with general supercritical growth ⋮ Stationary solitons of a three-wave model generated by type II second-harmonic generation in quadratic media ⋮ Fundamental properties and asymptotic shapes of the singular and classical radial solutions for supercritical semilinear elliptic equations ⋮ Uniqueness of positive solutions to some coupled cooperative variational elliptic systems ⋮ Erratum to “On the Classification of Standing Wave Solutions for the Schrödinger Equation” ⋮ Classification of solitary wave solutions to Schrödinger equations with potentials ⋮ Singular Solutions of the Scalar Field Equation with a Critical Exponent

Cites Work

• Ground state energy of the two-component charged Bose gas
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Asymptotic behavior of positive solutions of equation \(\Delta{} u+K(x)u^ p=0\) in \(\mathbb{R}{}^ n\)
• Singular solutions of the elliptic equation \(\Delta u- u+u^ p =0\)
• Separation property of solutions for a semilinear elliptic equation
• Monotonicity properties for ground states of the scalar field equation
• Structure of the sets of regular and singular radial solutions for a semilinear elliptic equation
• Uniqueness of Positive Radial Solutions of Δu + f(u) = 0 in ℝ n , II
• Nonexistence theorems for singular solutions of quasilinear partial differential equations
• Uniqueness of the ground state solutions of △u+f(u)=0 in Rⁿ, n≥3

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