Geodesic
Existence of positive solutions for s nonlinear three-point boundary value problem with integral boundary conditions
Habib Djourdem1 ; Slimane Benaicha1 ; Habib Djourdem ; Slimane Benaicha
1Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran, Oran
Acta mathematica Universitatis Comenianae, Tome 87 (2018) no. 2, pp. 167-177 
Habib Djourdem; Slimane Benaicha; Habib Djourdem; Slimane Benaicha. Existence of positive solutions for s nonlinear three-point boundary value problem with integral boundary conditions. Acta mathematica Universitatis Comenianae, Tome 87 (2018) no. 2, pp. 167-177. http://geodesic.mathdoc.fr/item/AMUC_2018_87_2_a1/
@article{AMUC_2018_87_2_a1,
     author = {Habib Djourdem and Slimane Benaicha and Habib Djourdem and Slimane Benaicha},
     title = { Existence of positive solutions for s nonlinear three-point boundary value problem with integral boundary conditions},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {167--177},
     year = {2018},
     volume = {87},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2018_87_2_a1/}
}
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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, $u(0)=u''(0)=0$, $ u(T)=\alpha\int_{0}^{\eta}ut(s) d s$, where $0<\eta, $0<\alpha<\frac{2T}{\eta^{2}}$ 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.