*(English)*Zbl 0647.35031

Summary: [For the entire collection see Zbl 0632.00014.]

We prove that if there exists a sub solution ${\psi}_{1}$, a strict super solution ${\varphi}_{1}$, a strict sub solution ${\psi}_{2}$, and a super solution ${\varphi}_{2}$ for

such that ${\psi}_{1}<{\varphi}_{1}<{\varphi}_{2}$, ${\psi}_{1}<{\psi}_{2}<{\varphi}_{2}$ and ${\psi}_{2}\nleqq {\varphi}_{1}$, then (1.1)-(1.2) has at least three distinct solutions ${u}_{s}$ $(s=1,2,3)$ such that ${\psi}_{1}\le {u}_{1}<{u}_{2}<{u}_{3}\le {\varphi}_{2}$. (Here we write ${z}_{1}<{z}_{2}$ when ${z}_{1}\le {z}_{2}$ and ${z}_{1}\ne {z}_{2}\xb7)$ This extends the work by *H. Amann* [SIAM Review 18, 620- 709 (1976; Zbl 0345.47044)] where the case ${\psi}_{1}<{\varphi}_{1}<{\psi}_{2}<{\varphi}_{2}$ was studied.