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Published online by Cambridge University Press: 29 November 2005
In this paper, general existence theorems are presented for the singular equation \[\left\{\begin{array}{@{}l}-(\varphi_p(u^{\prime}))^{\prime}=f(t,u,u^{\prime}),\;0<t<1\\[3pt]u(0)=u(1)=0.\end{array}\right.\] Throughout, our nonlinearity is allowed to change sign. The singularity may occur at $u=0,$$t=0$ and $t=1$.