Periodic segment implies infinitely many periodic solutions

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 Periodic Solutions for Nonautonomous Sublinear Second-Order Hamiltonian Systems

and Applied Analysis 3 Our main result is the following theorem. Theorem 1.1. Suppose that F t, x satisfies assumptions (A) and 1.7 . Assume that lim sup r→ ∞ inf x∈RN,|x| r |x|−2α ∫T 0 F t, x dt ∞, 1.8 lim inf R→ ∞ sup x∈RN,|x| R |x|−2α ∫T 0 F t, x dt −∞. 1.9

Infinitely many periodic solutions for some second-order differential systems with p(t)-Laplacian

* Correspondence: [email protected] School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, P. R. China Abstract In this article, we investigate the existence of infinitely many periodic solutions for some nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained using critical point theory. 2...

Sequences of Periodic Solutions and Infinitely Many Coexisting Attractors in the Border-Collision Normal Form

The border-collision normal form is a piecewise-linear continuous map on R N that describes dynamics near border-collision bifurcations of nonsmooth maps. This paper studies a codimension-three scenario at which the border-collision normal form with N = 2 exhibits infinitely many attracting periodic solutions. In this scenario there is a saddle-type periodic solution with branches of stable and...