Nontrivial periodic solutions of nonlinear functional differential systems with feedback control
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.
Anahtar Kelimeler:
Nonlinear functional differential equations with feedback control; Nontrivial periodic solutions; Leray-Schauder nonlinear alternative; Fixed point.
Nontrivial periodic solutions of nonlinear functional differential systems with feedback control
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.
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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