Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization

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....

Second-Order Boundary Value Problem with Integral Boundary Conditions

Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions

Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a function u, and prove that the set of bifurcation points for the solutions of the system is not σ-compact. Then, we deal with a linear system depending on a real parameter λ > 0 and on a function u, ...

On Second Order Differential Inclusions with Periodic Boundary Conditions

In this paper a fixed point theorem for condensing maps combined with upper and lower solutions are used to investigate the existence of solutions for second order differential inclusions with periodic boundary conditions.

Wave equation with second–order non–standard dynamical boundary conditions

The paper deals with the well–posedness of the problem 8 >< >: utt −∆u = 0 in R× Ω, utt = kuν on R× Γ, u(0, x) = u0(x), ut(0, x) = v0(x) in Ω, where u = u(t, x), t ∈ R, x ∈ Ω, ∆ = ∆x denotes the Laplacian operator respect to the space variable, Ω is a bounded regular (C∞) open domain of RN (N ≥ 1), Γ = ∂Ω, ν is the outward normal to Ω, k is a constant. We prove that it is ill–posed if N ≥ 2, wh...