Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 18 (2023), 343 -- 363

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

EXISTENCE OF POSITIVE SOLUTIONS OF A TERMINAL VALUE PROBLEM FOR FOURTH-ORDER DIFFERENTIAL EQUATIONS

Mohammed Dahmane and Mohammed Derhab

Abstract. We are concerned with the existence of positive solutions of a terminal value problem for a class of fourth-order differential equation. Our arguments are based to establish sufficient conditions which guarantee the existence of at least one positive solution by constructing a cone on which a positive operator is defined. We then apply a theorem of Guo-Krasonelskii to prove the existence of positive solutions of our problem.

2020 Mathematics Subject Classification: 47N20; 34B40; 34B18; 47H10
Keywords: Fourth order differential equation; positive solutions; Guo-Krasnoselskii theorem; cone preserving map.

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Mohammed Dahmane
Dynamic Systems and Applications Laboratory,
Department of Mathematics, Faculty of Sciences,
University Abou-Bekr Belkaid Tlemcen, B.P.119, Tlemcen, 13000, Algeria.
e-mail: dahmo_md@yahoo.fr

Mohammed Derhab
Dynamic Systems and Applications Laboratory,
Department of Mathematics, Faculty of Sciences,
University Abou-Bekr Belkaid Tlemcen, B.P.119, Tlemcen, 13000, Algeria.
e-mail: derhab@yahoo.fr

http://www.utgjiu.ro/math/sma