Further results on quasiperiodic partially localized solutions of homogeneous elliptic equations on \(\mathbb{R}^{N + 1} \)

DOI10.1016/j.jfa.2022.109457zbMath1489.35098OpenAlexW4221010442MaRDI QIDQ2123108

Darío A. Valdebenito, Peter Poláčik

Publication date: 8 April 2022

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2022.109457

zbMATH Keywords

existence of entire, quasiperiodic solutions, partially localized solutionssolutionshomogeneous elliptic equations

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear elliptic equations (35J61) Entire solutions to PDEs (35B08)

Cites Work

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• An energy constrained method for the existence of layered type solutions of NLS equations
• Multiplicity of layered solutions for Allen-Cahn systems with symmetric double well potential
• End-to-end construction for the Allen-Cahn equation in the plane
• Nonlinear scalar field equations. I: Existence of a ground state
• Saddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)
• On the existence of multi-transition solutions for a class of elliptic systems
• New classes of entire solutions for semilinear elliptic problems in \(\mathbb R^{n}\)
• The Toda system and multiple-end solutions of autonomous planar elliptic problems
• Multiple-end solutions to the Allen-Cahn equation in \(\mathbb R^2\)
• Uniqueness of non-negative solutions of semilinear equations in \({\mathbb{R}}^ n\)
• Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
• Saddle solutions of the bistable diffusion equation
• Uniqueness of positive solutions of \(\Delta u+f(u)=0\) in \(\mathbb{R}^N\), \(N\geqq 3\)
• Elliptic partial differential equations of second order
• On the uniqueness of the positive solution of a singularly perturbed problem
• On a class of reversible elliptic systems
• The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space
• Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems
• Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities for high frequencies
• Hamiltonian identities for elliptic partial differential equations
• Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
• Uniqueness of ground states for quasilinear elliptic equations
• Symmetry properties of some solutions to some semilinear elliptic equations
• Axial symmetry of some steady state solutions to nonlinear Schrödinger equations
• Uniqueness and nonuniqueness for positive radial solutions of Δu + f(u, r) = 0
• Uniqueness of the ground state solutions of △u+f(u)=0 in Rⁿ, n≥3
• Uniqueness of Radial Solutions of Semilinear Elliptic Equations
• More indices and bifurcations of positive solutions of Delta u + f(u) = 0 on R^N
• On the Helmholtz equation and Dancer’s-type entire solutions for nonlinear elliptic equations
• Non-uniqueness of positive ground states of non-linear Schrödinger equations
• New entire positive solution for the nonlinear Schrödinger equation: Coexistence of fronts and bumps
• Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on R^{N+1}
• Qualitative properties of some bounded positive solutions to scalar field equations