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

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 ...

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

Antiperiodic Solutions for Liénard-Type Differential Equation with p-Laplacian Operator

Antiperiodic problems arise naturally from the mathematical models of various of physical processes see 1, 2 , and also appear in the study of partial differential equations and abstract differential equations see 3–5 . For instance, electron beam focusing system in travelling-wave tube’s theories is an antiperiodic problem see 6 . During the past twenty years, antiperiodic problems have been s...

Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

New Boundary Value Problems for Higher Order Impulsive Fractional Differential Equations and Their Solvability

Firstly, the surveys for studies on boundary value problems for higher order ordinary differential equations and for higher order fractional differential equations are given. Secondly a simple review for studies on solvability of boundary value problems for impulsive fractional differential equations is presented. Thirdly we propose four classes of higher order linear fractional differential eq...