Turkish Journal of Mathematics
DOI
10.3906/mat-0810-46
Abstract
This paper examines the existence of nontrivial periodic solutions for the nonlinear functional differential system with feedback control: \{\aligned x'(t)=x(t)a(t)-\big[\sum_{i=1}^n a_i(t)\int_0^{+\infty} f(t, x(t-\theta)) d}\varphi_i(\theta) +\sum_{j=1}^m b_j(t) \int_0^{+\infty} f(t,x'(t-\theta))\,d}\phi_j(\theta)+\sum_{\mu=1}^p c_\mu(t) \int_0^{\infty} u(t-\theta)\,d}\delta_\mu(\theta)\big], u'(t)=-\rho(t)u(t)+\sum_{\nu=1}^q \beta_\nu(t) \int_0^{\infty} f(t, x(t-\theta))\,d}\psi_\nu(\theta).\endaligned Under certain growth conditions on the nonlinearity f, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative.
Keywords
Nonlinear functional differential equations with feedback control; Nontrivial periodic solutions; Leray-Schauder nonlinear alternative; Fixed point.
First Page
35
Last Page
44
Recommended Citation
GUO, YINGXIN
(2010)
"Nontrivial periodic solutions of nonlinear functional differential systems with feedback control,"
Turkish Journal of Mathematics: Vol. 34:
No.
1, Article 4.
https://doi.org/10.3906/mat-0810-46
Available at:
https://journals.tubitak.gov.tr/math/vol34/iss1/4
