Periodic boundary value problem for the second-order impulsive functional differential equations

Abstract

This paper considers the existence of extreme solutions of the periodic boundary value problems for the second order functional dzfferential equations The novelty zs that we introduce a new concept for lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative techmque is still valid Meanwhile, we extend previous results (~)

Second-order differential equations with deviating arguments

“…If n = 1, then from Lemma 2.2 we know that problems (3.2) have unique solutions y 1 and z 1 . We need to show that…”

Anti-periodic Boundary Value Problems of <i>φ</i>-Laplacian Impulsive Differential Equations

“…There has a significant development in impulse theory and impulsive differential equations (see [1,2,3]). Moreover, p-Laplacian operator arises in non-Newtonian fluid flows, turbulent filtration in porous media and in many other application areas (see [5,7] and references therein). Usually, p-Laplacian operator is replaced by abstract and more general version ϕ-Laplacian operator, which lead to clearer expositions and a better understanding of the methods which ware employed to derive the existence results (see [12,13]).…”

Boundary value problem for the second order impulsive delay differential equations

“…Among others the existence of solutions of the first and the second order impulsive functional differential equations by using the fixed point argument such as the Banach contraction principle, fixed point index theory and monotone iterative technique were discussed. We mention here the papers [1,2,3,4,5,7,8,9,12] and the references therein.…”