Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37In this paper we prove the existence of solutions for fractional impulsive differential equations with antiperiodic boundary condition in Banach spaces. The results are obtained by using fractional calculus' techniques and the fixed point theorems

Antiperiodic Problems for Nonautonomous Parabolic Evolution Equations

This work focuses on the antiperiodic problem of nonautonomous semilinear parabolic evolution equation in the form u′(t)=A(t)u(t)+f(t,u(t)), t∈R, u(t+T)=-u(t), t∈R, where (At)t∈R (possibly unbounded), depending on time, is a family of closed and densely defined linear operators on a Banach space X. Upon making some suitable assumptions such as the Acquistapace and Terreni conditions and exponential dichotomy on (At)t∈R, we obtain the existence results of antiperiodic mild solutions to such problem. The antiperiodic problem of nonautonomous semilinear parabolic evolution equation of neutral type is also considered. As sample of application, these results are applied to, at the end of the paper, an antiperiodic problem for partial differential equation, whose operators in the linear part generate an evolution family of exponential stability

Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions

This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of order α,β∈(4,5] with antiperiodic boundary conditions. Our results are based on the nonlinear alternative of Leray-Schauder type and the contraction mapping principle. Two illustrative examples are also presented

Evolution equations with nonlocal initial conditions and superlinear growth

We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as particular cases, the Cauchy multipoint problem, the weighted mean value problem and the periodic problem. The dynamic is transformed into an abstract setting and by combining an approximation technique with the Leray-Schauder continuation principle, we prove global existence results. By the compactness of the semigroup generated by the linear operator, we do not assume any Lipschitzianity, nor compactness on the nonlinear term or on the nonlocal initial condition. In addition, the exploited approximation technique coupled to a Hartman-type inequality argument, allows to treat nonlinearities with superlinear growth. Moreover, regarding the periodic case we are able to prove the existence of at least one periodic solution on the half line.Comment: 18 page