Multiple positive solutions for fractional boundary value problems with integral boundary conditions (Q6558068)

The authors study the existence of multiple positive solutions to a boundary value problem (BVP) of a second-order Riemann-Liouville fractional differential equation with an integral boundary condition, where the nonlinearity is assumed to be continuous. The boundary value problem is claimed to be equivalent to an integral equation. The fixed point theorem of cone expansion and compression and Leggett-Williams' fixed point theorem are used to the integral operator in the integral equation respectively to obtain the existence of positive solutions. An example is provided to show the application of the theoretic results.\N\NReviewer's remark: Lemma 2.1 of this paper needs extra conditions to ensure that the identity holds, see Remark 2.10 in [\textit{K. Lan}, Proc. Am. Math. Soc. 148, No. 12, 5225--5234 (2020; Zbl 1455.34007)]. Lemma 2.2 of this paper also needs extra conditions to ensure the existence and uniqueness, see Theorem 2.5 in [\textit{K. Lan}, Proc. Am. Math. Soc. 148, No. 12, 5225--5234 (2020; Zbl 1455.34007)].