We prove the existence of solutions for a second-order nonlinear impulsive boundary-value problem by applying Schaefer’s fixed point theorem. Results for periodic and anti-periodic impulsive boundary-value problems can be obtained as special cases of the results in this article.

In this paper, existence criteria for single and multiple positive solutions of periodic boundary value problems for first order difference equations of the form

The paper deals with the boundary value problem u ′′ + k u = g(u) + e(t), u(0) = u(2 ), u(0) = u(2 ), where k ∈ , g : (0,∞) 7→ is continuous, e ∈ [0, 2 ] and lim x→0+ 1 x g(s) ds = ∞. In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.

This article considers the extension of well-known discontinuous Galerkin (DG) finite element formulations to elliptic problems with periodic boundary conditions. Such problems routinely appear in a number of applications, particularly in homogenization of composite materials. We propose an approach in which the periodicity constraint is incorporated weakly in the variational formulation of the...

We study the periodic boundary value problem for semilinear fractional differential equations in an ordered Banach space. The method of upper and lower solutions is then extended. The results on the existence of minimal and maximal mild solutions are obtained by using the characteristics of positive operators semigroup and the monotone iterative scheme. The results are illustrated by means of a...