Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators

Rate of Decay of Stable Periodic Solutions of Duffing Equations

In this paper, we consider the second-order equations of Duffing type. Bounds for the derivative of the restoring force are given that ensure the existence and uniqueness of a periodic solution. Furthermore, the stability of the unique periodic solution is analyzed; the Supported in part by the science funds of Xi’an Jiaotong University Supported in part by the Xiao-Xiang Funds, Hunan Normal Un...

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 Variable Exponent Systems

Infinitely Many Large Energy Solutions of Superlinear Schrödinger-maxwell Equations

In this article we study the existence of infinitely many large energy solutions for the superlinear Schrödinger-Maxwell equations −∆u+ V (x)u+ φu = f(x, u) in R, −∆φ = u, in R, via the Fountain Theorem in critical point theory. In particular, we do not use the classical Ambrosetti-Rabinowitz condition.

Infinitely Many Strings in De Sitter Spacetime : Expanding and Oscillating Elliptic Function Solutions

The exact general evolution of circular strings in 2 + 1 dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter b, related to the string energy, and falls into three classes depending on whether b < 1/4 (oscillatory motion), b = 1/4 (degenerated, hyperbolic motion) or b > 1/4 (unbounded motion). The novel...