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On the Existence of Positive Solutions for the Time-Scale Dynamic Equations on Infinite Intervals

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

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Abstract

This paper investigates the existence of positive solutions to time-scale boundary value problems on infinite intervals. By applying the Leggett-Williams fixed point theorem in a cone, some new results for the existence of at least three positive solutions of boundary value problems are found. With infinite intervals, the theorem can be used to prove the existence of solutions of boundary value problems for nonlinear dynamic equations dependence on the delta derivative explicitly. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting.

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Acknowledgments

The author gratefully acknowledges Application Number 1919B021900156 of 2224-International Scientific Meetings Fellowship Programme 2019/1 by the Scientific and Technological Research Council of Turkey (TÜBİTAK).

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Computer Sciences, Abdullah Gul University, 38039, Kayseri, Turkey

    Abdulkadir Dogan

Authors
  1. Abdulkadir Dogan
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Correspondence to Abdulkadir Dogan .

Editor information

Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Dogan, A. (2020). On the Existence of Positive Solutions for the Time-Scale Dynamic Equations on Infinite Intervals. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_1

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