Positive solutions for a class of fractional boundary value problems - Xu, Jiafa; Wei, Zhongli (Nonlinear Analysis: Modelling and Control, 2016)
In this work, by virtue of the Krasnoselskii–Zabreiko fixed point theorem, we investigate the existence of positive solutions for a class of fractional boundary value problems under some appropriate conditions concerning the first eigenvalue of the relevant linear operator. Moreover, we utilize the method of lower and upper solutions to discuss the unique positive solution when the nonlinear term grows sublinearly.
Keywords: fractional boundary value problem; Krasnoselskii–Zabreiko fixed point theorem; positive solution; uniqueness