Existence Of Positive Solutions For Third-order Boundary Value Problems
Volume 4, Issue 1, pp 8 - 18
Publication Date: January 18, 2012
Authors
N. Nyamoradi
- Department of Mathematics, Faculty of Sciences Razi University, 67149 Kermanshah, Iran.
Abstract
In this work, by employing the Guo-Krasnoselskii fixed point theorem, we study the existence
of positive solutions to the third-order two-point non-homogeneous boundary value problem
\[
\begin{cases}
-u'''(t)=a(t)f(t,v(t)),\\
-v'''(t)=b(t)h(t,u(t)),\\
u(0)=u'(0)=0, \alpha u'(1)+\beta u''(1)=0,\\
v(0)=v'(0)=0, \alpha v'(1)+\beta v''(1)=0,
\end{cases}
\]
where \(\alpha\geq 0\) and \(\beta\geq 0\) with \(\alpha+\beta> 0\) are constant.
Keywords
- Positive solution
- Two-point boundary value problem
- Fixed point theorem.
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