Nontrivial periodic solutions of nonlinear functional differential systems with feedback control

作者：Guo, Yingxin^*

来源：Turkish Journal of Mathematics, 2010, 34(1): 35-44.

DOI：10.3906/mat-0810-46

• Nonlinear functional differential equations with feedback control
• Nontrivial periodic solutions
• Leray-Schauder nonlinear alternative
• Fixed point

This paper examines the existence of nontrivial periodic solutions for the nonlinear functional differential system with feedback control:
{x'(t)=x(t)a(t)-[Sigma(n)(i=1)a(i)(t) integral(+infinity)(0) f(t,x(t-theta))d phi(i)(theta)
+Sigma(m)(j=1)b(j)(t)integral(+infinity)(0) f(t,x'(t-theta))d phi(j)(theta) + Sigma(p)(mu=1) c(mu)(t) integral(infinity)(0) u(t-theta) d delta(mu)(theta)],
u'(t) = -rho(t)u(t) + Sigma(q)(v=1) beta(v)(t)integral(infinity)(0) f(t, x(t-theta)) d psi(v)(theta).
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.

• 出版日期2010
• 单位曲阜师范大学