Multiple positive solutions for higher order boundary value problems (Q1293510)

In many physical and biological problems only positive solutions are of interest. The author extends the work of \textit{L. H. Erbe}, \textit{S. Hu} and \textit{H. Wang} [J. Math. Anal. Appl. 184, No. 3, 640-648 (1994; Zbl 0805.34021)] to obtain two positive solutions to the boundary value problem \[ u^{(n)}+ f(t,u)= 0,\;0\leq t\leq 1,\;\alpha u^{(n- 2)}(0)- \beta u^{(n-1)}(0)= 0,\;\gamma u^{(n-2)}(1)+ \delta u^{(n-1)}(1)= 0, \] \[ u^{(i)}(0)= 0,\quad 0\leq i\leq n-3, \] when \(f\) is superlinear at one endpoint and sublinear at the other. An example is presented.