Positive solutions for nonlinear fractional differential equations with coefficient that changes sign

Abstract In this paper, we investigate the existence of positive solutions in case of the nonlinear fractional differential equation D s u = λ a ( t ) f ( u ) , 0 t 1 , where 0 s 1 , D s is the standard Riemann–Liouville fractional derivative, f : [ 0 , ∞ ) → [ 0 , ∞ ) , f ( 0 ) > 0 , a : [ 0 , 1 ] → ( - ∞ , + ∞ ) may change sign, and λ > 0 is a parameter. Our analysis relies on a nonlinear alternative of Leray–Schauder type.

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