A note on periodic solutions of some nonautonomous differential equations

1986 ◽  
Vol 34 (2) ◽  
pp. 253-265 ◽  
Author(s):  
M. R. Grossinho ◽  
L. Sanchez
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Time Dependent ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonautonomous Differential Equations ◽  
Nontrivial Periodic Solutions

We prove the existence of nontrivial periodic solutions of some nonlinear ordinary differential equations with time-dependent coefficients using variational methods.

CONTINUATION THEOREMS FOR AMBROSETTI-PRODI TYPE PERIODIC PROBLEMS

2000 ◽  
Vol 02 (01) ◽  
pp. 87-126 ◽  
Author(s):  
JEAN MAWHIN ◽  
CARLOTA REBELO ◽  
FABIO ZANOLIN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
A Priori ◽  
Nonlinear Ordinary Differential Equations ◽  
Type Problem ◽  
Normed Spaces ◽  
A Priori Bounds ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions

We study the existence of periodic solutions u(·) for a class of nonlinear ordinary differential equations depending on a real parameter s and obtain the existence of closed connected branches of solution pairs (u, s) to various classes of problems, including some cases, like the superlinear one, where there is a lack of a priori bounds. The results are obtained as a consequence of a new continuation theorem for the coincidence equation Lu=N(u, s) in normed spaces. Among the applications, we discuss also an example of existence of global branches of periodic solutions for the Ambrosetti–Prodi type problem u″+g(u)=s+ p(t), with g satisfying some asymmetric conditions.

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