Variational methods and boundary value problems for vector second order differential equations and applications to the pendulum equation

1984 ◽  
pp. 181-192 ◽  
Author(s):  
J. Mawhin ◽  
M. Willem
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Pendulum Equation

Boundary value problems for systems of second order differential equations

1985 ◽  
Vol 101 (1-2) ◽  
pp. 61-76 ◽  
Author(s):  
L. H. Erbe ◽  
H. W. Knobloch
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Existence Of A Solution ◽  
Differential Systems ◽  
Second Order Differential Equations

SynopsisWe consider boundary value problems for second order differential systems of the form (1)x” = A(t)x′ + f(t, x) and (2) x” = A(t)x′ + f(t, x) + q(t, x). By assuming the existence of a solution to (1) with a given region in (t, x) space, we derive conditions under which there exists a solution to (2) which stays in a certain neighbourhood of and satisfies given boundary conditions.

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