scholarly journals Existence of periodic solutions to second-order nonlinear ordinary differential equations

1974 ◽  
Vol 16 (1) ◽  
pp. 186-199 ◽  
Author(s):  
Robert E Gaines
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations ◽  
Existence Of Periodic Solutions

scholarly journals Periodic Solutions for Second-Order Ordinary Differential Equations with Linear Nonlinearity

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaohong Hu ◽  
Dabin Wang ◽  
Changyou Wang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Minimax Methods ◽  
Existence Of Periodic Solutions

By using minimax methods in critical point theory, we obtain the existence of periodic solutions for second-order ordinary differential equations with linear nonlinearity.

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.

On periodic boundary value problem for second-order ordinary differential equations

2019 ◽  
Vol 22 (06) ◽  
pp. 1950049
Author(s):  
Alexander Lomtatidze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Sufficient Conditions ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Nonautonomous Differential Equations ◽  
Existence Of Periodic Solutions

For second-order nonlinear nonautonomous differential equations, new sufficient conditions on the existence of periodic solutions are established.

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