The Existence of Triple Positive Solutions of Nonlinear Four-point Boundary Value Problem with p-Laplacian

This paper deals with the multiplicity results of positive solutions of one-dimensional singular p-Laplace equation ($\varphi_p(u'(t)))' + a{t)f(t,u(t),u'(t)) = 0$, 0 < t < 1 subject to the nonlinear boundary conditions $\alpha\varphi_p(u(0)) - \Beta\varphi_p(u'(\xi)) = 0$, $\gamma\varphi_p(u(1)) + \delta\varphi_p(u'(\eta)) = 0$ where $\varphi_p(x) = |x|^{p-2}x,p > 1$. By using the Avery-Peterson fixed point theorem, sufficient conditions for the existence of at least three positive solutions to the boundary value problem mentioned above are obtained.