Anti-periodic Boundary Value Conditions Research Articles

Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations

In this paper, we investigate the convergence of approximate solutions for a class of first-order integro-differential equations with antiperiodic boundary value conditions. By introducing the definitions of the coupled lower and upper solutions which are different from the former ones and establishing some new comparison principles, the results of the existence and uniqueness of solutions of the problem are given. Finally, we obtain the uniform and rapid convergence of the iterative sequences of approximate solutions via the coupled lower and upper solutions and quasilinearization method. In addition, an example is given to illustrate the feasibility of the method.

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

In this paper, we investigate the existence of solutions for a class of fractional boundary value problems with anti-periodic boundary value conditions with ψ-Caupto fractional derivative. By means of some standard fixed point theorems, sufficient conditions for the existence of solutions for the fractional differential inclusions with ψ-Caputo derivatives are presented. Our result generalizes the known special case if ψx=x and single known results to the multi-valued ones.

Second order differential variational inequalities involving anti-periodic boundary value conditions

This paper deals with a new class of second order nonlinear differential variational inequalities. Firstly, we study the properties of a solution set for a variational inequality by using the KKM technique and a monotonicity property. Then, we prove the existence of solutions to a second order nonlinear differential variational inequality with anti-periodic boundary value conditions not assuming the Lipschitz continuity of the nonlinear term. Our approaches, which are essentially different from previous research methods in differential variational inequalities, are based on the topological degree theory and the Filippov implicit function lemma.

Antiperiodic solutions of fourth‐order impulsive differential equation

In this paper, the existence of antiperiodic solutions for fourth‐order impulsive differential equation is obtained by variational approaches and results on the auxiliary system. It is interesting that there is no growth restraint on nonlinear terms and impulsive terms. Besides, any minimizing sequence is bounded in a closed convex set of a space composed of Lipschitzian functions with the appearance of antiperiodic boundary value conditions.

Boundary value problems for semilinear differential inclusions of fractional order in a Banach space

In the present paper, we show that the solution set of a fractional order semilinear differential inclusion in a Banach space has the topological structure of an -set. This result allows to apply a fixed point result for condensing multimaps to the translation multioperator along the trajectories of such inclusion and to prove the existence of solutions satisfying periodic and anti-periodic boundary value conditions. An example concerning with a fractional order feedback control system is presented.

The existence of solution for a k-dimensional system of fractional differential inclusions with anti-periodic boundary value conditions

We investigate the existence of solutions for a k-dimensional systems of fractional differential inclusions with anti-periodic boundary conditions. We provide two results via different conditions for obtaining solutions of the k-dimensional inclusion problem. We provide some examples to illustrate our results.

Anti-periodic boundary value problems of fractional differential equations with the Riemann-Liouville fractional derivative

In this paper, the author puts forward a kind of anti-periodic boundary value problems of fractional equations with the Riemann-Liouville fractional derivative. More precisely, the author is concerned with the following fractional equation: with the anti-periodic boundary value conditions where denotes the standard Riemann-Liouville fractional derivative of order , and the nonlinear function may be singular at . By applying the contraction mapping principle and the other fixed point theorem, the author obtains the existence and uniqueness of solutions. MSC:34A08, 34B15.

Existence results for anti-periodic boundary value problems of fractional differential equations

In this paper, the author is concerned with the fractional equation with the anti-periodic boundary value conditions where denotes the Caputo fractional derivative of order γ, the constants α, , , , satisfy the conditions , , . Different from the recent studies, the function f involves the Caputo fractional derivative and . In addition, the author put forward new anti-periodic boundary value conditions, which are more suitable than those studied in the recent literature. By applying the Banach contraction mapping principle and the Leray-Schauder degree theory, some existence results of solutions are obtained. MSC:34A08, 34B15.

Antiperiodic Boundary Value Problem for Second-Order Impulsive Differential Equations on Time Scales

We prove the existence results for second-order impulsive differential equations on time scales with antiperiodic boundary value conditions in the presence of classical fixed point theorems.

On the Solvability of Second-Order Impulsive Differential Equations with Antiperiodic Boundary Value Conditions

We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.

Anti-periodic boundary value problems for first order impulsive functional differential equations

This paper considers existence of solutions for a class of first order functional differential equation with anti-periodic boundary value conditions. We introduce new concept of lower and upper solutions which is quite different from the former one. And we present that monotone iterative technique coupled with lower and upper solutions is still valid.

Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations

We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general n th problem in time scales with linear dependence on the i th Δ-derivatives for i = 1,2,…,n, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of the equation is defined by a function f(t,x) which is rd-continuous in t and continuous in x uniformly in t. To do that, we obtain the expression of the Green's function of a related linear operator in the space of the antiperiodic functions.