摘要：In this paper, we study the existence and multiplicity of solutions of the quasilinear problems with minimum and maximum $$\begin{aligned}& \bigl(\phi \bigl(u'(t)\bigr)\bigr)'=(Fu) (t),\quad \mbox{a.e. }t\in (0,T), \\& \min \bigl\{ u(t) \mid t\in [0,T]\bigr\} =A, \qquad \max \bigl\{ u(t) \mid t\in [0,T]\bigr\} =B, \end{aligned}$$ where $\phi :(-a,a)\rightarrow \mathbb{R}$ ($0 1$ is a constant and $A, B\in \mathbb{R}$ satisfy $B>A$. By using the Leray–Schauder degree theory and the Brosuk theorem, we prove that the above problem has at least two different solutions.
