Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions

Infinitely Many Coexisting Sinks from Degenerate Homoclinic Tangencies

The evolution of a horseshoe is an interesting and important phenomenon in Dynamical Systems as it represents a change from a nonchaotic state to a state of chaos. As we are interested in determining how this transition takes place, we are studying certain families of diffeomorphisms. We restrict our attention to certain one-parameter families {Ft} of diffeomorphisms in two dimensions. It is as...

Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a Homoclinic Tangency

We study the problem of coexistence of a countable number of periodic orbits of different topological types (saddles, saddle–centers, and elliptic) in the case of four-dimensional symplectic diffeomorphisms with a homoclinic trajectory to a saddle–focus fixed point.

Infinitely Many Periodic Solutions for Variable Exponent Systems

Infinitely Many Periodic Solutions of Nonlinear Wave Equations on S

The existence of time periodic solutions of nonlinear wave equations utt −∆nu + ` n− 1 2 ́2 u = g(u)− f(t, x) on n-dimensional spheres is considered. The corresponding functional of the equation is studied by the convexity in suitable subspaces, minimax arguments for almost symmetric functional, comparison principles and Morse theory. The existence of infinitely many time periodic solutions is o...

Infinitely Many Homoclinic Solutions for Second Order Nonlinear Difference Equations with p-Laplacian

We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discrete p-Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations.