Solution of a boundary value problem for a nonlinear system of second order ordinary differential equations

1969 ◽  
Vol 20 (1) ◽  
pp. 30-39 ◽  
Author(s):  
Yu. I. Kovach ◽  
L. I. Savchenko
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value ◽  
Second Order

scholarly journals Multiple solutions of boundary value problem

2006 ◽  
Vol 37 (2) ◽  
pp. 149-154
Author(s):  
Yongjin Li ◽  
Xiaobao Shu ◽  
Yuantong Xu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Group Index ◽  
Variational Structure

By means of variational structure and $ Z_2 $ group index theory, we obtain multiple solutions of boundary value problems for second-order ordinary differential equations$ \begin{cases} & - (ru')' + qu = \lambda f(t, u),\qquad 0 < t < 1 \\ & u'(0) = 0 = \gamma u(1)+ u'(1), \qquad \text{ where } \gamma \geq 0. \end{cases} $

scholarly journals Periodic boundary value problem for second order integro-ordinary differential equations with general kernel and Carathéodory nonlinearities

1995 ◽  
Vol 18 (4) ◽  
pp. 757-764 ◽  
Author(s):  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Extremal Solutions ◽  
Monotone Method

We study the existence of solutions for the periodic boundary value problem for some second order integro-differential equations with a general kernel. Also we develop the monotone method to approximate the extremal solutions of the problem.

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