In this paper, classical and enriched finite element formulations to impose Bloch-periodic boundary conditions are proposed. Bloch-periodic boundary conditions arise in the description of wave-like phenomena in periodic media. We consider the quantum-mechanical problem in a crystalline solid, and derive the weak formulation and matrix equations for the Schrödinger and Poisson equations in a par...

In the case of not requiring the nonlinear term to be monotone or convex, we study the existence of positive solutions for second-order periodic boundary value problem by using the first eigenvalue of the corresponding linear problem and fixed point index theory. The work significantly improves and generalizes the main results of J. Graef et al. [A periodic boundary value problem with vanishing...

In this work, the authors consider the boundary value problem { y + a(t)y = g(t) f (y), 0 ≤ t ≤ 2π, y(0) = y(2π), y(0) = y(2π), and establish the existence of nonnegative solutions in the case where the associated Green’s function may have zeros. The results are illustrated with an example. c © 2007 Elsevier Ltd. All rights reserved.

the purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of sturm-liouville problem with equation of the form w??=(?2f(x)?r(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in c2(a,b which has a single zero (so called turning point) at point 0x=x and r(x) is a continuously differentiable function. ...

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.