Electron. J. Differential Equations,
Vol. 2018 (2018), No. 158, pp. 1-11.
Local extrema of positive solutions of nonlinear functional
differential equations
George E. Chatzarakis, Lana Horvat Dmitrovic, Mervan Pasic
Abstract:
We study the positive solutions of a general class of second-order functional
differential equations, which includes delay, advanced, and delay-advanced
equations. We establish integral conditions on the coefficients on a given
bounded interval J such that every positive solution has a local maximum in
J. Then, we use the connection between that integral condition and
Rayleigh quotient to get a sufficient condition that is easier to be applied.
Several examples are provided to demonstrate the importance of our results.
Submitted May 17, 2018. Published August 31, 2018.
Math Subject Classifications: 34A30, 34B30, 34C10, 34C11.
Key Words: Functional differential equations; local non-monotonicity;
integral criteria; Rayleigh quotient; delay; advance;
super-sub linear nonlinearity.
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George E. Chatzarakis
Department of Electrical and Electronic Engineering Educators
School of Pedagogical and Technological Education (ASPETE)
14121, N. Heraklio, Athens, Greece
email: geaxatz@otenet.gr, gea.xatz@aspete.gr
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Lana Horvat Dmitrovic
Department of Mathematics
Faculty of Electrical Engineering and Computing
University of Zagreb
Unska 3, 10000 Zagreb, Croatia
email: Lana.Horvat@fer.hr
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Mervan Pasic
Department of Mathematics
Faculty of Electrical Engineering and Computing
University of Zagreb
Unska 3, 10000 Zagreb, Croatia
email: mervan.pasic@fer.hr
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