Pseudo S-Asymptotically(ω,c)-Periodic Solutions to Fractional Differential Equations of Sobolev Type

In this paper,we firstly recall some basic results on pseudo S-asymptotically(ω,c)-periodic functions and Sobolev type fractional differential equation.We secondly investigate some existence of pseudo S-asymptotically(ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type.We finally present a simple example.

Existence and uniqueness of S-asymptotically periodic α-mild solutions for neutral fractional delayed evolution equation

In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establish the existence and uniqueness of the S-asymptotically periodic α-mild solutions. The linear part generates a compact and exponentially stable analytic semigroup and the nonlinear parts satisfy some conditions with respect to the fractional power norm of the linear part, which greatly improve and generalize the relevant results of existing literatures.

Existence of Exactly n+1 Simple 4-Periodic Solutions of the Differential Delay Equation x(t)=-f(x(t-1))

By discussing the zeros of periodic.solutions we give in this paper a criterion for the existence of exactly n+1 simple 4-periodic solutions of the differential delay equation x(T)= -f(x(t-1)).

2π-PERIODIC SOLUTION OF THE EQUATION x + f(x)x + bx + g(x(t - т)) = p(t)

In this paper, time delay Lienard's equations are considered, by using the theory of concidence degree, a sufficient condition of existence of at least one 2π-periodic solution is obtained.

Pseudo asymptotically periodic solutions for fractional integro-differential neutral equations

In this paper, we study the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of class r for fractional integro-differential neutral equations. An example is presented to illustrate the application of the abstract results.

Weighted Pseudo Asymptotically Periodic Mild Solutions of Evolution Equations

In this paper, we propose a new class of functions called weighted pseudo S-asymptotically periodic function in the Stepanov sense and explore its properties in Banach space including composition theorems. Furthermore, the existence, uniqueness of the weighted pseudo S-asymptotically periodic mild solutions to partial evolution equations and nonautonomous semilinear evolution equations are investigated. Some interesting examples are presented to illustrate the main findings.

PERIODIC SOLUTIONS OF A CLASS OF EVEN ORDER DIFFERENTIAL EQUATIONS

We investigate sufficient conditions (theorem 1) for the non-existence of periodic solutions of ecluatlon (2. 1 ) with P = 0 and sufficient, conditions (theorem 2) for existencc of periodic solutions of equation (1. 1. 1 ).