Publicación: NON-TRIVIAL PERIODIC SOLUTIONS FOR A CLASS OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH LARGE DELAY
Fecha
2023
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ACTA APPLICANDAE MATHEMATICAE
Resumen
WE PROVIDE A RESULT ON THE EXISTENCE OF A POSITIVE PERIODIC SOLUTION FOR THE FOLLOWING CLASS
OF DELAY EQUATIONS
0´(T) -0(T) + F (0(T - R)) = 0.
IN PARTICULAR, WE FIND AN INFINITE FAMILY OF DISJOINT INTERVALS HAVING THE FOLLOWING PROPERTY:
IF THE DELAY IS WITHIN ONE OF THESE INTERVALS, THEN THE EQUATION ADMITS A NON-TRIVIAL AND EVEN
2R-PERIODIC SOLUTION. FURTHERMORE, THE LENGTH OF THESE INTERVALS IS CONSTANT AND DEPENDS ON
THE SIZE OF THE TERM |F (?)|, WHERE ? IS THE UNIQUE POSITIVE EQUILIBRIUM POINT OF THE EQUATION.
CONSEQUENTLY, WE CAN FIND PERIODIC SOLUTIONS FOR ARBITRARILY LARGE DELAYS.
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Periodic solutions, Non-perturbative methods, Differential delay equation, Degree theory
