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On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays
2012
Abstract and Applied Analysis
The existence results of positiveω-periodic solutions are obtained for the second-order functional differential equation with multiple delaysu″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),...,u(t−τn(t))), wherea(t)∈C(ℝ)is a positiveω-periodic function,f:ℝ×[0,+∞)n+1→[0,+∞)is a continuous function which isω-periodic int, andτ1(t),...,τn(t)∈C(ℝ,[0,+∞))areω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.
doi:10.1155/2012/929870
fatcat:zz43h563mvdqxoxsvqsp5kcyoi