Global Existence for Semilinear Evolution Equations with Nonlocal Conditions

Existence of Mild Solutions for Nonlocal Semilinear Fractional Evolution Equations

In this paper, we investigate a class of semilinear fractional evolution equations with nonlocal initial conditions given by (1) ⎧⎨ ⎩ dqu(t) dtq = Au(t)+(Fu)(t), t ∈ I, u(0)+g(u) = u0, where 0 < q< 1 , I is a compact interval. Sufficient conditions for the existence of mild solutions for the equation (1) are derived. The main tools include Laplace transform, Arzela-Ascoli’s Theorem, Schauder’s ...

Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions

Existence of Solutions for Semilinear Differential Equations with Nonlocal Conditions in Banach Spaces

This paper is concerned with semilinear differential equations with nonlocal conditions in Banach spaces. Using the tools involving the measure of noncompactness and fixed point theory, existence of mild solutions is obtained without the assumption of compactness or equicontinuity on the associated linear semigroup.

Existence of Mild Solutions of Semilinear Evolution Inclusions with Nonlocal Conditions

The existence of mild solutions of first order semilinear evolution inclusions on a compact real interval is investigated in Banach spaces with nonlocal conditions. A fixed point theorem for condensing maps due to Martelli is used. 2000 Mathematics Subject Classification: 34A60, 34G20, 35R10, 47H20

Semilinear Volterra Integrodifferential Equations with Nonlocal Initial Conditions

where h ∈ L1(0,T ;X) and f : [0,T ]×X →X. This is obtained if one takes F(u)(t)= h(t)−∫ t 0 a(t−s)f (s,u(s))ds in (1.1). Such problems are important from the viewpoint of applications since they cover nonlocal generalizations of integrodifferential equations arising in the mathematical modeling of heat conduction in materials with memory. Byszewski [6, 7] initiated the work concerning abstract ...