No abstract

In this work we obtain some new results concerning the existence of solutions to an impulsive first-order, nonlinear ordinary differential equation with periodic boundary conditions. The ideas involve differential inequalities and Schaefer's fixed-point theorem.

Abstract. Shooting methods are employed to obtain solutions of the threepoint boundary value problem for the second order equation, y = f (x, y, y ), y(x 1 ) = y 1 , y(x 3 ) − y(x 2 ) = y 2 , where f : (a, b) × R 2 → R is continuous, a < x 1 < x 2 < x 3 < b, and y 1 , y 2 ∈ R, and conditions are imposed implying that solutions of such problems are unique, when they exist.

No abstract

This work formulates existence, uniqueness, and uniqueness-implies-existence theorems for solutions to two-point vector boundary value problems on time scales. The methods used include maximum principles, a priori bounds on solutions, and the nonlinear alternative of Leray-Schauder