On the existence of periodic solutions for the third-order nonlinear ordinary differential equations

1999 ◽  
Vol 14 (2) ◽  
pp. 125-130 ◽  
Author(s):  
Huang Xiankai
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Nonlinear Ordinary Differential Equations ◽  
Third Order ◽  
The Third ◽  
Existence Of Periodic Solutions

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.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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