On Positive Periodic Solutions to Nonlinear Fifth-Order Differential Equations with Six Parameters

Abstract EN

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.