Axial symmetry of some steady state solutions to nonlinear Schrödinger equations

DOI10.1090/S0002-9939-2010-10638-XzbMath1211.35115OpenAlexW2014357145MaRDI QIDQ3085066

Andrea Malchiodi, Hao-yuan Xu, Changfeng Gui

Publication date: 28 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10638-x

zbMATH Keywords

nonlinear Schrödinger equationsteady state solutionaxial symmetrymoving plane methodHamiltonian identity

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Second-order elliptic equations (35J15) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Related Items (13)

Layered solutions to the vector Allen-Cahn equation in \(\mathbb{R}^2\). Minimizers and heteroclinic connections ⋮ Further results on quasiperiodic partially localized solutions of homogeneous elliptic equations on \(\mathbb{R}^{N + 1} \) ⋮ Gradient Lagrangian systems and semilinear PDE ⋮ Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems ⋮ Symmetry of some entire solutions to the Allen-Cahn equation in two dimensions ⋮ An energy constrained method for the existence of layered type solutions of NLS equations ⋮ On the Helmholtz equation and Dancer’s-type entire solutions for nonlinear elliptic equations ⋮ Properties of solutions to semilinear elliptic problem with Hardy potential ⋮ Symmetry of traveling wave solutions to the Allen-Cahn equation in \({\mathbb R^{2}}\) ⋮ Symmetry of separable functions and its applications to Choquard type equations ⋮ ASYMPTOTIC AXISYMMETRY OF THE SUBSONIC TRAVELING WAVES TO THE GROSS–PITAEVSKII EQUATION ⋮ Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on R^{N+1} ⋮ The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space

Cites Work

• Unnamed Item
• Hamiltonian constants for several new entire solutions
• On the uniqueness of the positive solution of a singularly perturbed problem
• Symmetry of traveling wave solutions to the Allen-Cahn equation in \({\mathbb R^{2}}\)
• Hamiltonian identities for elliptic partial differential equations
• Symmetry of Entire Solutions to the Allen-Cahn Equation
• Qualitative properties of some bounded positive solutions to scalar field equations

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