MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Existence of a positive solution for a third-order three point boundary value problem
Ali Rezaiguia and Smail Kelaiaia

Abstract

By applying the Krasnoselskii fixed point theorem in cones and the fixed point index theory, we study the existence of positive solutions of the non linear third-order three point boundary value problem $u'''(t)+a(t)f(t,u(t))=0$, $t\in(0,1)$; $u'(0)=u'(1)=\alpha u(\eta)$, $u(0)=\beta u(\eta)$, where $\alpha$, $\beta$ and $\eta$ are constants with $\alpha\in[0,\frac{1}{\eta})$, and $0<\eta<1$. The results obtained here generalize the work of Torres [Positive solution for a third-order three point boundary value problem, Electronic J. Diff. Equ. 2013 (2013), 147, 1--11].

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Keywords: Third-order differential equations; three point boundary value problem; Krasnoselski fixed point in a cone; fixed point index theory

MSC: 34B10

Pages:  12--25     

Volume  68 ,  Issue  1 ,  2016