## Abstract

We use the inequalities of Holder, Gronwall and Wirtinger type to establish sufficient conditions for that the null function is the unique nonnegative solution of some integral inequalities. Such conditions are useful to guarantee compactness properties of Monch and Palais-Smale type for integral operators on spaces of vector-valued functions. An applications to superlinear boundary value problems in Hilbert spaces is also presented.

## Authors

**Radu Precup**

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

## Keywords

Inequality involving derivatives; compactness: Papais-Smale condition; nonlinear integral operator; fixed point; critical point theory; boundary value problem.

## Paper coordinates

R. Precup, *Inequalities and compactness*, In: “Inequalities Theory and Applications”, Y.J. Cho, J.K. Kim, S.S. Dragomir eds., Nova Science Publ., Huntington-New York, 2001, 257-271.

## About this paper

##### Journal

##### Publisher Name

Nova Science Publ.

##### DOI

##### Print ISSN

##### Online ISSN

MR 2065320.

google scholar link

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