Existence of positive solutions for s nonlinear three-point boundary value problem with integral boundary conditions

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Habib Djourdem Slimane Benaicha

Abstract

We investigate the existence of positive solutions to the nonlinearthird-order three-point integral boundary value problem  $u'''(t)+a(t)f(t,u(t))=0$,          $ 0<t<T$,   $u(0)=u''(0)=0$,       $ u(T)=\alpha\int_{0}^{\eta}ut(s) d s$,   where   $0<\eta<T$,   $0<\alpha<\frac{2T}{\eta^{2}}$   are given constants.We show the existence of at least one positive solution if   $f$   iseither superlinear or sublinear by applying Krasnoselskii'sfixed point theorem in cones.

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How to Cite
Djourdem, H., & Benaicha, S. (2018). Existence of positive solutions for s nonlinear three-point boundary value problem with integral boundary conditions. Acta Mathematica Universitatis Comenianae, 87(2), 167-177. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/901/619
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