Positivity and lower and upper solutions for fourth order boundary value problems (Q885334)

The authors are concerned with existence and multiplicity of solutions of the fourth order boundary value problem \[ u^{(4)}=f(t,u(t)),\quad t\in [0,1], \quad u(0)=u(1)=u''(0)=u''(1)=0 \] in the presence of a pair of, not necessarily ordered, lower and upper solutions. The proof of the main results are based upon maximum principles and Amann's three solutions theorem [see \textit{H. Amann}, J. Funct. Anal. 11, 346--384 (1972; Zbl 0244.47046)].