Local extrema of positive solutions of nonlinear functional differential equations
Date
2018-08-31
Authors
Chatzarakis, George
Horvat Dmitrovic, Lana
Pasic, Mervan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Functional differential equations, Local non-monotonicity, Integral criteria, Rayleigh quotient, Delay, Advance, Super-sub linear nonlinearity
Citation
Chatzarakis, G. E., Horvat Dmitrović, L., & Pasic, M. (2018). Local extrema of positive solutions of nonlinear functional differential equations. <i>Electronic Journal of Differential Equations, 2018</i>(158), pp. 1-11.
Rights
Attribution 4.0 International