Multiplicity of positive solutions for a fourth-order quasilinear singular differential equation

摘要

This paper is concerned with the multiplicity of positive solutions of boundary value problem for the fourth-order quasilinear singular differential equation $$ (|u''|^{p-2}u'')''=lambda g(t)f(u),quad 00$. We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of positive solutions. We have found a threshold $lambda^*<+infty$, such that if $0