- Turkish Journal of Mathematics
- Vol: 34 Issue: 1
- Nontrivial periodic solutions of nonlinear functional differential systems with feedback control
Nontrivial periodic solutions of nonlinear functional differential systems with feedback control
Authors : Yingxin Guo
Pages : 35-44
View : 8 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
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[\sumi=1n ai(t)\int0+\infty f(t, x(t-q)) d}ji(q) +\sumj=1m bj(t) \int0+\infty f(t,x'(t-q))\,d}fj(q)+\summ=1p c\mu(t) \int0\infty u(t-q)\,d}d\mu(q)\big], u'(t)=-r(t)u(t)+\sumn=1q b\nu(t) \int0\infty f(t, x(t-q))\,d}y\nu(q).\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.