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 ON THREE-POINT BOUNDARY VALUE PROBLEM

2016 ◽  
Vol 21 (2) ◽  
pp. 270-281
Author(s):  
Nadezhda Sveikate
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations ◽  
Point Boundary

Three-point boundary value problems for the second order nonlinear ordinary differential equations are considered. Existence of solutions are established by using the quasilinearization approach. As an application, the Emden-Fowler type problems with nonresonant and resonant linear parts are considered to demonstrate our results.

Existence theorems for equations in normed spaces and boundary value problems for nonlinear vector ordinary differential equations

1984 ◽  
Vol 98 (1-2) ◽  
pp. 1-11 ◽  
Author(s):  
A. Cañada ◽  
R. Ortega
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Linear Part ◽  
Sufficient Conditions ◽  
First Eigenvalue ◽  
Normed Spaces ◽  
Nonlinear Vector

SynopsisThe existence of solutions to equations in normed spaces is proved when the nonlinear part of the equation satisfies growth and asymptotic conditions, whether the linear part is invertible or not. For this, we use the coincidence degree theory developed by Mawhin. We apply our abstract results to boundary value problems for nonlinear vector ordinary differential equations. In particular, we consider the Picard boundary value problem at the first eigenvalue and the periodic boundary value problem at resonance. In both cases, the nonlinear term can be of superlinear type. Also, necessary and sufficient conditions of Landesman-Lazer type are obtained.

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