# Existence of Positive Solutions for Third-order Boundary Value Problems

Volume 4, Issue 1, pp 8--18
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### 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.

•  34B18

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