Homoclinic solutions for linear and linearizable ordinary differential equations.
Homoclinic solutions for second-order non-autonomous Hamiltonian systems without global Ambrosetti-Rabinowitz conditions.
Homoclinic solutions of 2nth-order difference equations containing both advance and retardation
By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.
Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries.
Lower and upper bounds for the splitting of separatrices of a pendulum under a fast quasiperiodic forcing.
Maslov index for homoclinic orbits of hamiltonian systems
Melnikov deviations and limit cycles for Lienard equations
Multibump solutions for a class of lagrangian systems slowly oscillating at infinity
Multibump solutions for an almost periodically forced singular Hamiltonian system.
Multichain-type solutions for Hamiltonian systems.
Multiple solutions of nonlinear boundary value problems for equations with critical points
Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems
We prove the existence of infinitely many geometrically distinct homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems.
Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity
On connecting orbits of semilinear parabolic equations on .
On geometric detection of periodic solutions and chaotic dynamics.
On the existence of homoclinic solutions for almost periodic second order systems
Orbites Hétérocliniques au Voisinage d'une Bifurcation de Poincaré Dégénérée pour les Champs de Vecteurs de ...
Orbits connecting singular points in the plane
This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed.
Poincaré-Melnikov theory for n-dimensional diffeomorphisms
We consider perturbations of n-dimensional maps having homo-heteroclinic connections of compact normally hyperbolic invariant manifolds. We justify the applicability of the Poincaré-Melnikov method by following a geometric approach. Several examples are included.
Quadratic systems with homoclinic cycles described by quintic curves.