Multiple solutions for \((n,p)\) boundary value problems (Q2761988)

Let \(-y^{(n)}=f(t,y)\) be an \(n\)th-order differential equation satisfying the boundary conditions \(y^{(i)}(0)=0\), \(0\leq i\leq n-2\); \(y^{( p)}(1) =0\), where \(n\geq 2\) and \(p\) is a fixed integer satisfying \(0\leq p\leq n-1\). It is assumed that \(f(t,y)\) is a continuous nonnegative function on \([0,1]\times [0,\infty)\) and \(f(t,y)\not\equiv 0\) on any subinterval of \([0,1]\) and for all \(0\leq y<\infty\). The authors impose growth conditions on \(f\) such that the above mentioned boundary value problem has an arbitrary number of positive solutions.