Second order adjoint matrix equations

On Self-Adjoint Differential Equations of Second Order.

Behavior of Solutions of Second Order Self- Adjoint Differential Equations

Principal Quadratic Functionals and Self-Adjoint Second-Order Differential Equations.

Homoclinic orbits for second order self-adjoint difference equations

In this paper we discuss how to use variational methods to study the existence of nontrivial homoclinic orbits of the following nonlinear difference equations Δ [ p(t)Δu(t − 1)]+ q(t)u(t)= f (t, u(t)), t ∈Z, without any periodicity assumptions on p(t), q(t) and f , providing that f (t, x) grows superlinearly both at origin and at infinity or is an odd function with respect to x ∈R, and satisfie...

Oscillation Results for Second Order Self-adjoint Matrix Differential Systems

on [0,∞), where Y (t), P (t) and Q(t) are n × n real continuous matrix functions on [0,∞) with P (t), Q(t) symmetric and P (t) positive definite for t ∈ [0,∞) (P (t) > 0, t ≥ 0). A solution Y (t) of (1.1) is said to be nontrivial if det Y (t) 6= 0 for at least one t ∈ [0,∞) and a nontrivial solution Y (t) of (1.1) is said to be prepared (selfconjugated) if Y ∗(t)P (t)Y ′(t)− Y ∗′(t)P (t)Y (t) ≡...