Periodic solutions for nonlinear evolution equations at resonance

Anti-periodic solutions for nonlinear evolution equations

*Correspondence: [email protected] 1Fundamental Department, Aviation University of Air Force, Changchun, 130022, People’s Republic of China Full list of author information is available at the end of the article Abstract In this paper, we use the homotopy method to establish the existence and uniqueness of anti-periodic solutions for the nonlinear anti-periodic problem { ẋ + A(t, x) + Bx = f (t) ...

Periodic Solutions for Nonlinear Evolution Equations in a Banach Space

We prove an existence result for 7"-periodic mild solutions to nonlinear evolution equations of the form u(t) + Au(t) BF(t, u(t)) , t€R+. y Here (X, \\-\\) is a real Banach space, A: D(A) C X —> 2 is an operator with A — a! m-accretive for some a > 0 and such that -A. generates a compact semigroup, while F: R+ x D(A) —► X is a Carathéodory mapping which is T-periodic with respect to its first a...

Recurrent Dimensions of Quasi-periodic Solutions for Nonlinear Evolution Equations

In this paper we introduce recurrent dimensions of discrete dynamical systems and we give upper and lower bounds of the recurrent dimensions of the quasi-periodic orbits. We show that these bounds have different values according to the algebraic properties of the frequency and we investigate these dimensions of quasi-periodic trajectories given by solutions of a nonlinear PDE.

Periodic solutions for evolution equations ∗

We study the existence and uniqueness of periodic solutions for evolution equations. First we analyze the one-dimensional case. Then for arbitrary dimensions (finite or not), we consider linear symmetric operators. We also prove the same results for non-linear sub-differential operators A = ∂φ where φ is convex.

Solutions of Nonlinear Hyperbolic Equations at Resonance