Existence and exact asymptotic behaviour of positive solutions for fractional boundary value problem with P-Laplacian operator

ABSTRACT This paper deals with existence, uniqueness and global behaviour of a positive solution for the fractional boundary value problem Dβ(ψ(x)Φp(Dαu))=a(x)uσ in (0,1) with the condition limx→0Dβ？1(ψ(x)Φp(Dαu(x)))=limx→1ψ(x)Φp(Dαu(x))=0andlimx→0Dα？1u(x)=u(1)=0, where β,α∈(1,2], Φp(t)=t|t|p？2, p>1, σ∈(1？p,p？1), the differential operator is taken in the Riemann–Liouville sense and ψ,a :(0,1)？R are non-negative and continuous functions that may are singular at x=0 or x=1 and satisfies some appropriate conditions