Existence of positive solutions for a $p$-Laplacian equation with applications to Hematopoiesis

This paper is concerned with the existence of at least one   positive solution for a boundary value problem (BVP), with  $p$-Laplacian, of the form    begin{equation*}        begin{split}            (Phi_p(x^{'}))^{'} + g(t)f(t,x)  &= 0, quad t     in (0,1),\            x(0)-ax^{'}(0) = alpha[x], & quad            x(1)+bx^{'}(1) = beta[x],        end{split}    end{equation*}where $Phi_{p}(x) = |x|^{p-2}x$ is a one dimensional $p$-Laplacian operator with $p>1, a,b$ are real constants and $alpha,beta$ are  the Riemann-Stieltjes integrals    begin{equation*}        begin{split}            alpha[x] = int limits_{0}^{1} x(t)dA(t), quad  beta[x] = int limits_{0}^{1} x(t)dB(t),        end{split}    end{equation*}with $A$ and $B$ are functions of bounded variation. A Homotopy version of  Krasnosel'skii fixed point theorem is used to prove our results.