Multiplicity results of breathers for the discrete nonlinear Schrödinger equations with unbounded potentials

DOI10.1007/s11425-014-4883-2zbMath1328.39011OpenAlexW1983552090MaRDI QIDQ2515307

Zhan Zhou, Defang Ma

Publication date: 31 July 2015

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-014-4883-2

zbMATH Keywords

critical point theorybreathersmultiplicity resultsdiscrete nonlinear Schrödinger equationsunbounded potentials

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Additive difference equations (39A10) Discrete version of topics in analysis (39A12)

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Cites Work

• Unnamed Item
• Unnamed Item
• Homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity
• Existence of breather solutions of the DNLS equations with unbounded potentials
• Existence and multiplicity results for the nonlinear Schrödinger-Poisson systems
• Discrete nonlinear Schrödinger equations with superlinear nonlinearities
• Homoclinic solutions in periodic difference equations with saturable nonlinearity
• Traveling waves in Fermi-Pasta-Ulam lattices with saturable nonlinearities
• Existence of solutions for \(p(x)\)-Laplacian equations with singular coefficients in \(\mathbb R^N\)
• Gap solitons in periodic discrete Schrödinger equations with nonlinearity
• On the existence of homoclinic solutions of a class of discrete nonlinear periodic systems
• Heteroclinic orbits and heteroclinic chains for a discrete Hamiltonian system
• Breathers in nonlinear lattices: existence, linear stability and quantization
• Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity
• Existence of gap solitons in periodic discrete nonlinear Schrödinger equations
• Centre manifold reduction for quasilinear discrete systems
• Minimax theorems
• Existence and multiplicity results of homoclinic solutions for the DNLS equations with unbounded potentials
• Multibreathers in Klein-Gordon chains with interactions beyond nearest neighbors
• Travelling waves of forced discrete nonlinear Schrödinger equations
• Gap solitons in periodic discrete nonlinear Schrödinger equations. II: A generalized Nehari manifold approach
• Discrete breathers: localization and transfer of energy in discrete Hamiltonian nonlinear systems
• Periodic and decaying solutions in discrete nonlinear Schrödinger with saturable nonlinearity
• On the existence of gap solitons in a periodic discrete nonlinear Schrödinger equation with saturable nonlinearity
• Travelling waves of discrete nonlinear Schrödinger equations with nonlocal interactions
• Standing wave solutions of the discrete non-linear Schrödinger equations with unbounded potentials, II
• Breather solutions of the discrete nonlinear Schrödinger equations with unbounded potentials
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• Periodic motions of an infinite lattice of particles with nearest neighbor interaction
• Gap solitons in periodic discrete nonlinear Schrödinger equations
• Variant fountain theorems and their applications
• Variational proof for hard discrete breathers in some classes of Hamiltonian dynamical systems.

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