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)  &= ۰, \quad t     \in (۰,۱),\\            x(۰)-ax^{'}(۰) = \alpha[x], & \quad            x(۱)+bx^{'}(۱) = \beta[x],        \end{split}    \end{equation*}where \Phi_{p}(x) = |x|^{p-۲}x is a one dimensional p-Laplacian operator with p>۱, a,b are real constants and \alpha,\beta are  the Riemann-Stieltjes integrals    \begin{equation*}        \begin{split}            \alpha[x] = \int \limits_{۰}^{۱} x(t)dA(t), \quad  \beta[x] = \int \limits_{۰}^{۱} 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.

Keywords:

Fixed point , positive solution , p-Laplacian , non-local boundary conditions , Boundary value problem