On Positive Periodic Solutions to Nonlinear Fifth-Order Differential Equations with Six Parameters. (16th March 2016) - Wang, Yunhai; Wang, Fanglei
Abstract : We study the existence and multiplicity of positive periodic solutions to the nonlinear differential equation: u 5 ( t ) + k u 4 ( t ) - β u 3 - ξ u ″ ( t ) + α u ' ( t ) + ω u ( t ) = λ h ( t ) f ( u ), i n 0 ≤ t ≤ 1, u i ( 0 ) = u i ( 1 ), i = 0, 1, 2, 3, 4, where k, α, ω, λ > 0, β, ξ ∈ R, h ∈ C ( R, R ) is a 1-periodic function. The proof is based on the Krasnoselskii fixed point theorem.