In this paper we use the well-known Schauder fixed point principle to obtain the existence of square-mean almost periodic solutions to some classes of nonautonomous second order stochastic differential equations on a Hilbert space.

A one dimensional stochastic differential equation of the form dX = AXdt+ 1 2 (−A) ∂ξ[((−A)X)]dt+ ∂ξdW (t), X(0) = x is considered, where A = 1 2∂ 2 ξ . The equation is equipped with periodic boundary conditions. When α = 0 this equation arises in the Kardar–Parisi–Zhang model. For α 6= 0, this equation conserves two important properties of the Kardar–Parisi–Zhang model: it contains a quadratic...

In this work, we consider a new model describing the survival of red blood cells in animals. Specifically, we study a class of Lasota-Wazewska equation with pseudo almost periodic varying environment and mixed delays. By using the Banach fixed point theorem and some inequality analysis, we find sufficient conditions for the existence, uniqueness and stability of solutions. We generalize some re...

This paper is concerned with the existence of almost periodic and pseudo almost solutions for a nonlinear integro-differential equation with neutral delay, which arise in epidemic problems. By using almost periodic functions theory and fixed point theory, we obtain the results. Two examples are given to illustrate our results. In addition, an application to nonautonomous differential equations ...

We study the existence of solutions for a class of fractional differential inclusions with anti-periodic boundary conditions. The main result of the paper is based on Bohnenblust-Karlins fixed point theorem. Some applications of the main result are also discussed.

We show a Cr connecting lemma for area-preserving surface diffeomorphisms and for periodic Hamiltonian on surfaces. We prove that for a generic Cr , r = 1, 2, . . ., ∞, area-preserving diffeomorphism on a compact orientable surface, homotopic to identity, every hyperbolic periodic point has a transversal homoclinic point. We also show that for a Cr, r = 1, 2, . . ., ∞ generic time periodic Hami...

In this article, we study sufficient conditions for existence and uniqueness of positive solutions to the following coupled system of fractional order differential equations with antiperiodic boundary conditions { cDαu(t)+ f (t,v(t), Dα−1v(t)) = 0, cDβ v(t)+g(t,u(t), Dβ−1u(t)) = 0, 0 < t < 1, u(0) = −u(1),v(0) = −v(1), Du(0) = −Dpu(1), Dv(0) = −Dqv(1), where 1 < α ,β 2,α − p 1,β − q 1 and 0 < p...

Existence and approximation of best proximity points is an interesting topic for which one can see [2, 3, 4, 6, 5] for more information. Another extension of Banach contraction principle was given by Nieto and Rodriguez-Lopez in partially ordered metric spaces [9]. They proved some fixed point theorems in partially ordered sets in order to show the existence and uniqueness for a first-order ord...

In this paper, we prove the existence of solutions for an anti-periodic boundary value problem of nonlinear impulsive fractional differential equations by applying some known fixed point theorems. Some examples are presented to illustrate the main results.