Multiple positive solutions of saturable nonlinear Schrödinger equations with intensity functions

DOI10.3934/dcds.2020110zbMath1436.35097OpenAlexW3003569013MaRDI QIDQ1988308

Tsung-fang Wu, Tai-Chia Lin

Publication date: 16 April 2020

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2020110

zbMATH Keywords

variational methodsnonlinear Schrödinger equationsexistence of multiple positive solutions

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Schrödinger operator, Schrödinger equation (35J10) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09)

Related Items (2)

Normalized solutions of quasilinear Schrödinger equations with saturable nonlinearity ⋮ Localization of normalized solutions for saturable nonlinear Schrödinger equations

Cites Work

• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Asymptotically linear Schrödinger equation with potential vanishing at infinity
• Symmetry and related properties via the maximum principle
• The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function.
• Four positive solutions for the semilinear elliptic equation: \(-\Delta u+u=a(x) u^p +f(x)\) in \(\mathbb{R}^N\)
• The virial theorem and ground state energy estimates of nonlinear Schrödinger equations in \(\mathbb{R}^2\) with square root and saturable nonlinearities in nonlinear optics
• On the variational principle
• A note on asymptotically linear elliptic problems in \(\mathbb R^N\)
• Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities
• The principle branch of solutions of a nonlinear elliptic eigenvalue problem on \(\mathbb{R}^ N\)
• Minimax theorems
• Orbital stability and energy estimate of ground states of saturable nonlinear Schrödinger equations with intensity functions in \(\mathbb{R}^2\)
• Dual variational methods in critical point theory and applications
• Uniqueness of ground states for quasilinear elliptic equations
• On the shape of least‐energy solutions to a semilinear Neumann problem
• Critical points and nonlinear variational problems
• Applying the mountain pass theorem to an asymptotically linear elliptic equation on R^N
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• A positive solution for an asymptotically linear elliptic problem on $\mathbb{R}^N$ autonomous at infinity
• A remark on least energy solutions in $\mathbf {R}^N$
• Existence of a positive solution of an elliptic equation on R^N
• The existence of a positive solution to asymptotically linear scalar field equations
• Ground states of nonlinear Schrödinger systems with saturable nonlinearity in $\mathbb {R}^2$R2 for two counterpropagating beams
• On a class of asymptotically linear elliptic problems in \(\mathbb R^N\)

This page was built for publication: Multiple positive solutions of saturable nonlinear Schrödinger equations with intensity functions