Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations

In this paper we make a subtle use of operator theory techniques and the well-known Schauder fixed-point principle to establish the existence of pseudo-almost automorphic solutions to some second-order damped integro-differential equations with pseudo-almost automorphic coefficients. In order to illustrate our main results, we will study the existence of pseudo-almost automorphic solutions to a structurally damped plate-like boundary value problem.Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:1402.563

Existence of positive S-asymptotically periodic solutions of the fractional evolution equations in ordered Banach spaces

In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable

Existence and global asymptotic behavior of S-asymptotically periodic solutions for fractional evolution equation with delay

This paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study the existence of S-asymptotically periodic mild solutions under the situation that the relevant semigroup is noncompact and the nonlinear term satisfies more general growth conditions instead of Lipschitz-type conditions. Moreover, by establishing a new Gronwall-type integral inequality corresponding to fractional differential equation with delay, we consider the global asymptotic behavior of S-asymptotically periodic mild solutions, which will make up for the blank of this field

S-asymptotically ω-periodic solutions in the p-th mean for a Stochastic Evolution Equation driven by Q-Brownian motion

International audienceIn this paper, we study the existence (uniqueness) and asymptotic stability of the p-th mean S-asymptotically ω-periodic solutions for some non-autonomous Stochastic Evolution Equations driven by a Q-Brownian motion. This is done using the Banach fixed point Theorem and a Gron-wall inequality