Modern Problems in Applied Analysis pp 203-214 | Cite as

# Positive Solutions for a Nonlocal Resonant Problem of First Order

## Abstract

We study a first order differential system subject to a nonlocal condition. Our goal in this paper is to establish conditions sufficient for the existence of positive solutions when the considered problem is at resonance. The key tool in our approach is Leggett-Williams norm-type theorem for coincidences due to O’Regan and Zima. We conclude the paper with several examples illustrating the main result.

## Keywords

Positive solution Cone Resonant problem Nonlocal condition## Mathematics Subject Classification (2010)

Primary 34B18; Secondary 34B10## Notes

### Acknowledgements

This work was completed with the partial support of the Centre for Innovation and Transfer of Natural Science and Engineering Knowledge of University of Rzeszów. The author wishes to express her thanks to the referees for careful reading of the manuscript and constructive comments.

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