## Abstract

We are concerned with the study of semilinear evolution equations with nonlocal initial conditions. We provide sufficient conditions on the nonlinearity which allow the use of variants of the nonlinear alternative to prove the existence of at least one solution. Our second result presents a novel growth condition splitted into two parts, one for the subinterval containing the points involved by the initial conditions, and another for the rest of the interval.

## Authors

**Abdelkader Boucherif
**Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

**Radu Precup**

Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

Evolution equation; Nonlocal initial condition; Mild solution; Fixed point.

## Paper coordinates

A. Boucherif, R. Precup, *Semilinear evolution equations with nonlocal initial conditions*, Dynamic Systems Appl. 16 (2007), 507-516.

## About this paper

##### Journal

Dynamic Systems and Applications

##### Publisher Name

##### Print ISSN

##### Online ISSN

1056-2176

google scholar link

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