Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

الملخص EN

We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments D α x ( t ) + μ h ( t ) f ( x ( a ( t ) ) ) = 0 , t ∈ ( 0,1 ) , 2 < α ≤ 3 , μ > 0 , x ( 0 ) = x ′ ( 0 ) = 0 , x ( 1 ) = β x ( η ) + λ [ x ] , β > 0 , and η ∈ ( 0,1 ) , where D α is the standard Riemann-Liouville derivative, f : [ 0 , ∞ ) → [ 0 , ∞ ) is continuous, f ( 0 ) > 0 , h : [ 0,1 ] → ( − ∞ , + ∞ ) , and a ( t ) is the advanced argument.

Our analysis relies on a nonlinear alternative of Leray-Schauder type.

An example is given to illustrate our results.