Displaying similar documents to “Continuity, compactness, fixed points, and integral equations.”

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.