Periodic solutions for nonlinear equations with mean curvature-like operators

THE REVIEW OF ALMOST PERIODIC SOLUTIONS TO A STOCHASTIC DIERENTIAL EQUATION

This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.  

Periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argument

where τ , e ∈ C(R,R) are T-periodic, and f , g ∈ C(R × R,R) are T-periodic in the first argument, T >  is a constant. In recent years, there are many results on the existence of periodic solutions for various types of delay differential equation with deviating arguments, especially for the Liénard equation and Rayleigh equation (see [–]). Now as the prescribed mean curvature ( x ′(t) √ +x′...

Existence and stability of almost periodic solutions to impulsive stochastic differential equations

This paper introduces the concept of square-mean piecewise almost periodic for impulsive stochastic processes. The existence of square-mean piecewise almost periodic solutions for linear and nonlinear impulsive stochastic differential equations is established by using the theory of the semigroups of the operators and Schauder fixed point theorem. The stability of the square-mean piecewise almos...

Existence and Uniqueness of Periodic Solutions for a Class of Nonlinear Equations with p-Laplacian-Like Operators

We investigate the following nonlinear equations with p-Laplacian-like operators φ x′ t ′ f x t x′ t g x t e t : some criteria to guarantee the existence and uniqueness of periodic solutions of the above equation are given by using Mawhin’s continuation theorem. Our results are new and extend some recent results due to Liu B. Liu, Existence and uniqueness of periodic solutions for a kind of Lie...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY