Displaying similar documents to “Existence of triple positive periodic solutions of a functional differential equation depending on a parameter.”

On the existence of one-signed periodic solutions of some differential equations of second order

Jan Ligęza (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We study the existence of one-signed periodic solutions of the equations x ' ' ( t ) - a 2 ( t ) x ( t ) + μ f ( t , x ( t ) , x ' ( t ) ) = 0 , x ' ' ( t ) + a 2 ( t ) x ( t ) = μ f ( t , x ( t ) , x ' ( t ) ) , where μ > 0 , a : ( - ∞ , + ∞ ) → ( 0 , ∞ ) is continuous and 1-periodic, f is a continuous and 1-periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.

Existence of periodic solutions for first-order totally nonlinear neutral differential equations with variable delay

Abdelouaheb Ardjouni, Ahcène Djoudi (2014)

Commentationes Mathematicae Universitatis Carolinae

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We use a modification of Krasnoselskii’s fixed point theorem due to Burton (see [Liapunov functionals, fixed points and stability by Krasnoselskii’s theorem, Nonlinear Stud. 9 (2002), 181–190], Theorem 3) to show that the totally nonlinear neutral differential equation with variable delay x ' ( t ) = - a ( t ) h ( x ( t ) ) + c ( t ) x ' ( t - g ( t ) ) Q ' ( x ( t - g ( t ) ) ) + G ( t , x ( t ) , x ( t - g ( t ) ) ) , has a periodic solution. We invert this equation to construct a fixed point mapping expressed as a sum of two mappings such that one is compact and the other is a large contraction. We show that the...