In this paper, we prove a theorem on the existence of solutions for a second
order differential inclusion governed by the Clarke subdifferential of a
Lipschitzian function and by a mixed semicontinuous perturbation.
Abstract
This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem
$$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$
where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.
We study the existence of solutions for the periodic boundary value problem for some second order integro-differential equations with a general kernel. Also we develop the monotone method to approximate the extremal solutions of the problem.
Abstract
Using Mawhin's continuation principle we obtain a general result on the existence of solutions to a boundary value problem for second order nonlinear vector ODEs. Applications are given to the existence of solutions which are contained in suitable bound sets with possibly non-smooth boundary.
This paper is concerned with the existence of solutions for the discrete second-order boundary value problemΔ2u(t-1)+λ1u(t)+g(Δu(t))=f(t),t∈{1,2,…,T},u(0)=u(T+1)=0, whereT>1is an integer,f:{1,…,T}→R,g:R→Ris bounded and continuous, andλ1is the first eigenvalue of the eigenvalue problemΔ2u(t-1)+λu(t)=0,t∈T,u(0)=u(T+1)=0.
AbstractIn this work, we investigate the existence of solutions for a class of second order impulsive differential equations using either the implicit function theorem or bifurcation techniques by the mean of Krasnosel'ski theorem.
On second order nonlocal boundary value problem at resonance
