Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1168.34310
Meng, Fanchao; Du, Zengji
Solvability of a second-order multi-point boundary value problem at resonance.
(English)
[J] Appl. Math. Comput. 208, No. 1, 23-30 (2009). ISSN 0096-3003

Summary: Based on the coincidence degree theory of Mawhin, we get a general existence result for the following second-order multi-point boundary value problem at resonance $$x''(t)= f(t,x(t),x'(t))+e(t), \quad t\in(0,1),$$ $$x(0)= \sum_{i=1}^m \alpha_ix(\xi_i), \qquad x'(1)= \sum_{j=1}^n \beta_jx'(\eta_j),$$ where $f:[0,1]\times\Bbb R^2\to\Bbb R$ is a Carathéodory function, $e\in L^1[0,1]$, $0<\xi_1<\xi_2<\cdots< \xi_m<1$, $\alpha_i\in\Bbb R$, $i=1,2,\dots,m$, $m\ge 2$ and $0<\eta_1<\cdots<\eta_n<1$, $\beta_j\in\Bbb R$, $j=1,\dots,n$, $n\ge 1$. In this paper, both of the boundary value conditions are responsible for resonance.
MSC 2000:
*34B10 Multipoint boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: multi-point boundary value problem; coincidence degree theory; resonance

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster