Dergiler / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 1
Nontrivial periodic solutions of nonlinear functional differential systems with feedback control
- Sayfa
- 35–44
- DOI
- —
Özet
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.
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.