Global solutions for a functional second order abstract Cauchy problem with nonlocal conditions

Existence Results for a Second-order Abstract Cauchy Problem with Nonlocal Conditions

In this paper we study the existence of mild and classical solutions for a second-order abstract Cauchy problem with nonlocal conditions.

Second-order Sufficient Optimality Conditions for a Semilinear Optimal Control Problem with Nonlocal Radiation Interface Conditions

We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffusegray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local op...

A third-order nonlocal problem with nonlocal conditions

A Second-order Impulsive Cauchy Problem

We study the existence of mild and classical solutions for an abstract second-order impulsive Cauchy problem modeled in the form ü(t) = Au(t)+f(t,u(t),u̇(t)), t ∈ (−T0,T1), t ≠ ti; u(0) = x0, u̇(0) = y0; u(ti) = I1 i (u(ti)), u̇(ti) = I2 i (u̇(t+ i )), where A is the infinitesimal generator of a strongly continuous cosine family of linear operators on a Banach space X and f , I1 i , I 2 i are appro...

An Abstract Cauchy Problem for Higher Order Functional Differential Inclusions with Infinite Delay

The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our ...