Barriers in impulsive antiperiodic problems

Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations

Impulsive differential equations, which arise in biology, physics, population dynamics, economics, and so forth, are a basic tool to study evolution processes that are subjected to abrupt in their states see 1–4 . Many literatures have been published about existence of solutions for first-order and second-order impulsive ordinary differential equations with boundary conditions 5–19 , which are ...

On a New Class of Antiperiodic Fractional Boundary Value Problems

and Applied Analysis 3 where g(t, s) is g (t, s) = {{{{{{{{{{{{{{ {{{{{{{{{{{{{{ { (t − s) q−1 − (1/2) (T − s) q−1 Γ (q) + (T − 2t) (T − s) q−2 4Γ (q − 1) + t (T − t) (T − s) q−3 4Γ (q − 2) , s ≤ t, − (T − s) q−1 2Γ (q) + (T − 2t) (T − s) q−2 4Γ (q − 1) + t (T − t) (T − s) q−3 4Γ (q − 2) , t < s. (14) If we let p → 1− in (7), we obtain G T (t, s) 󵄨󵄨󵄨󵄨p→1− = {{{{{{{{{{{{{{{{{{{ {{{{{{{{{{{{{{{{{...

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

Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known that many biological phenomena involving threshold, bursting rhythm models in medicine and biology, optimal control models in economics,...

Antiperiodic Boundary Value Problems for Finite Dimensional Differential Systems

The study of antiperiodic solutions for nonlinear evolution equations is closely related to the study of periodic solutions, and it was initiated by Okochi 1 . During the past twenty years, antiperiodic problems have been extensively studied by many authors, see 1–31 and the references therein. For example, antiperiodic trigonometric polynomials are important in the study of interpolation probl...

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