A variant of the mountain pass theorem and variational gluing

DOI10.1007/s00032-020-00318-3zbMath1471.35124OpenAlexW3082423381MaRDI QIDQ2027280

Piero Montecchiari, Paul H. Rabinowitz

Publication date: 25 May 2021

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-020-00318-3

zbMATH Keywords

mountain pass theoremvariational methodsHamiltonian systemshomoclinic solutionsdouble well potentialnondegeneracy conditionheteroclinic solutionsmultitransition solutionsvariational gluing

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Second-order elliptic systems (35J47) Boundary value problems for second-order elliptic systems (35J57)

Related Items (2)

Normalized multi-bump solutions of nonlinear Schrödinger equations via variational approach ⋮ Non-minimizing connecting orbits for multi-well systems

Cites Work

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• A double well potential system
• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Extensions of Moser-Bangert theory. Locally minimal solutions
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• A variational approach to homoclinic orbits in Hamiltonian systems
• On the existence of multi-transition solutions for a class of elliptic systems
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Extensions of the mountain pass theorem
• A mountain pass theorem
• Minimal solutions of variational problems on a torus
• On minimal laminations of the torus
• Corrections to: Vector-valued local minimizers of nonconvex variational problems
• Looking for the Bernoulli shift
• Variational construction of connecting orbits
• On global non-degeneracy conditions for chaotic behavior for a class of dynamical systems
• Solutions of mountain pass type for double well potential systems
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Existence and multiplicity of homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems
• On a class of reversible elliptic systems
• Pseudoholomorphic curves and the shadowing lemma
• Prescribed energy connecting orbits for gradient systems
• Dual variational methods in critical point theory and applications
• A nondegeneracy condition for a semilinear elliptic system and the existence of 1- bump solutions
• Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs
• A minimum-maximum principle for a class of non-linear integral equations
• Multiplicity results for a class of semilinear elliptic equations on \(\mathbb{R}^ m\)
• On the connection problem for potentials with several global minima
• A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain-Pass Theorem
• Calculus of variations in the large and classical mechanics
• The Structure of the Critical Set in the Mountain Pass Theorem
• Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials
• Homoclinic type solutions for a semilinear elliptic PDE on ℝⁿ
• Existence of infinitely many homoclinic orbits in Hamiltonian systems

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