A discontinuous functional Cauchy problem

Weighted Cauchy-type problem of a functional differ-integral equation

In this work, we are concerned with a nonlinear weighted Cauchy type problem of a differ-integral equation of fractional order. We will prove some local and global existence theorems for this problem, also we will study the uniqueness and stability of its solution.

A singular abstract cauchy problem.

In this note a singular abstract Cauchy problem is considered. A solution is obtained for this problem in terms of a regular abstract Cauchy problem. As an application we obtain a new solution of the initial value problem for a class of singular partial differential equations.

Inhomogeneous Two-Parameter Abstract Cauchy Problem

Lectures on Cauchy Problem

No part of this book may be reproduced in any form by print, microfilm or any other means without written permission from the

Stability of a Semilinear Cauchy Problem

This paper is contributed to the Cauchy problem  ∂u ∂t = ∆u+K(|x|)u p in R × (0, T ), u(x, 0) = φ(x) in R, (0.1) with initial function φ 6≡ 0. The stability and instability of the positive radical steady states, which are positive solutions of ∆u+K(|x|)u = 0, (0.2) has been discussed with different assumption on K(x) and φ under the norm ∗Research supported in part by the Natural Science...