## Abstract

We study the existence and uniqueness of equations

u′′(t)=f(t,u(t),u′(t),u(g₁(t)),…,u(g_{m}(t))) 1.1

u(t)=p(t),)t∈I╲intI,(1.2)

in a Banach space. This problem is regarded as a particular case of the Dirichlet problem

xxx

We study the existence and uniqueness of equations

\(u\prime\prime(t)=f(t,u(t),u\prime(t),u(g\U{2081} (t)),\ldots,u(g\_\{m\}(t))))\ 1.1

\(u(t)=p(t),)t\in I\diagdown intI)\,(1.2)

in a Banach space. This problem is regarded as a particular case of the

Dirichlet problem

??

for the differential equation

??

The main result regarding the existence of the solution of problem

??

is contained in Theorem 1, where the mapping in the right hand side must obey

a weaker condition than being compact.

This condition is expressed with the aid of Kuratowski noncompactness measure.

## Authors

Radu **Precup****
**”University Babeș-Bolyai” Cluj-Napoca, Romania

## Keywords

?

##### Cite this paper as:

R. Precup, *Measure of noncompactness and second order differential equations with deviating argument*, Studia Univ. Babeş-Bolyai Math., 34 (1989) no. 2, pp. 25-35.

## About this paper

##### Journal

Studia Universitatis Babes-Bolyai Mathematica

##### Publisher Name

Babes-Bolyai University

##### DOI

Not available yet.

##### Print ISSN

Not available yet.

##### Online ISSN

Not available yet.

MR: 91k:34094.

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