SHARP ASYMPTOTIC ANALYSIS OF POSITIVE SOLUTIONS OF A COMBINED STURM-LIOUVILLE PROBLEM

Authors

  • S. Belkahla Faculty of Sciences, University of Tunis el Manar, Tunisia Author
  • Z. Zine El Abidine Higher School of Sciences and Technology of Hammam Sousse, University of Sousse, Tunisia Author

DOI:

https://doi.org/10.57016/MV-XFOQ5120

Keywords:

Asymptotic analysis, Sturm-Liouville equation, Dirichlet problem, Green function, Karamata class, Schäuder's fixed point theorem

Subjects:

26A12, 34B16, 34B18, 34B27

Abstract

In this work, we investigate a class of nonlinear combined Sturm-Liouville problems with zero Dirichlet boundary conditions. Using the Karamata regular variation theory and the Sch{a}uder fixed point theorem, we prove the existence of a unique positive solution satisfying a precise asymptotic behavior where a competition between singular and non singular terms in the nonlinearity appears.

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Published

2023-01-15

Issue

Vol. 75 No. 1 (2023): Vol. 75, Issue 1

Section

Articles

License

Copyright (c) 2023 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.