Existence of solutions to a Kirchhoff ψ-Hilfer fractional p-Laplacian equations

In this paper, using the genus properties in critical point theory, we study the existence and multiplicity of solutions to the following Kirchhoff psi-Hilfer fractional p-Laplacian: {a+b integral(T)(0)vertical bar D-H(0+)alpha,beta;psi xi(x)vertical bar(p)dx)D-H(T)alpha,beta;psi (vertical bar D-H(0+)alpha,beta;psi xi(x)vertical bar(p-2) D-H(0+)alpha,beta;psi xi(x)) -lambda vertical bar xi(x)vertical bar(p-2) xi(x) = g(x,xi(x)), I-0+(beta(beta-1);psi) xi(0) = I-T(beta(beta-1);psi) xi(T), where D-H(0+)alpha,beta;psi xi(x) and D-H(T)alpha,beta;psi are psi-Hilfer fractional derivatives left-sided and right-sided of order 1/p < alpha < 1, a, b > 0 are constants, 0 <= beta <= 1 and I-0+(beta(beta-1);psi) (.) and I-T(beta(beta-1);psi) (.) are psi-Riemann-Liouville fractional integrals left-sided and right-sided, and g :[0.T] x R -> R is a continuous function.