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