The existence of multiple positive periodic solutions for functional differential equations. (English) Zbl 1167.34371
Summary: The existence of multiple positive solutions for the integral equation
\[ x(t)= \int _t ^{t+\omega}G(t,s)b(s)f(s,x(s-\tau_1(s)),\dots , x(s-\tau_n(s)))ds \]
is studied by using fixed point index theory. Using these results we obtain new results on the existence of multiple positive periodic solutions for some first order periodic functional differential equations.
\[ x(t)= \int _t ^{t+\omega}G(t,s)b(s)f(s,x(s-\tau_1(s)),\dots , x(s-\tau_n(s)))ds \]
is studied by using fixed point index theory. Using these results we obtain new results on the existence of multiple positive periodic solutions for some first order periodic functional differential equations.
MSC:
| 34K13 | Periodic solutions to functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
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