Existence and concentration of solutions to the Gross-Pitaevskii equation with steep potential well

DOI10.1007/s00033-021-01510-0zbMath1466.35177OpenAlexW3136415976MaRDI QIDQ2026493

Hui-Fang Jia, Xiao Luo

Publication date: 19 May 2021

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-021-01510-0

zbMATH Keywords

variational methodsGross-Pitaevskii equationdipolar quantum gasessteep potential well

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of solitary waves in dipolar quantum gases
• Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in \(\mathbb{R}^3\)
• Bound states for semilinear Schrödinger equations with sign-changing potential
• Existence and multiplicity of solutions for the Kirchhoff equations with asymptotically linear nonlinearities
• On the existence of solutions for the Schrödinger-Poisson equations
• Positive solutions for nonlinear Schrödinger equations with deepening potential well
• Minimax theorems
• Multibump solutions of nonlinear Schrödinger equations with steep potential well and indefinite potential
• Concentrating standing waves for the Gross-Pitaevskii equation in trapped dipolar quantum gases
• Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
• Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates
• Strong instability of standing waves for the nonlinear Schrödinger equation in trapped dipolar quantum gases
• On Dipolar Quantum Gases in the Unstable Regime
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• On the Gross–Pitaevskii equation for trapped dipolar quantum gases
• NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL
• Derivation of the Dipolar Gross--Pitaevskii Energy
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases
• GLOBAL BRANCH OF SOLUTIONS FOR NON-LINEAR SCHRÖDINGER EQUATIONS WITH DEEPENING POTENTIAL WELL

This page was built for publication: Existence and concentration of solutions to the Gross-Pitaevskii equation with steep potential well