Twin solutions to right focal \((1,n-1)\) singular boundary value problems (Q2784731)

The author proves the existence of two nonnegative solutions to the \((1,n-1)\) right focal BVP with \(n\geq 2\). Particularly, the author studies the \(n\)th-order differential equation NEWLINE\[NEWLINE (-1)^{n-1}y^{(n)}(t)=\phi(t)[g(y(t))+h(y(t))], \leqno (1) NEWLINE\]NEWLINE and the focal boundary conditions NEWLINE\[NEWLINE y(0)=0, \quad y^{(i)}(1), \quad 1\leq i\leq n-1. \leqno (2) NEWLINE\]NEWLINE Here, \(\phi\in C(0,1)\cap L[0,1]\) is positive on \((0,1)\), \(g\in C(0,\infty)\) is positive, nonincreasing on \((0,\infty)\) and may be singular at \(y=0\), \(h\in C[0,\infty)\) is nonnegative on \((0,\infty)\) and \({h\over g}\) is nondecreasing on \((0,\infty)\). NEWLINENEWLINENEWLINEAdditional conditions on \(\phi, g\) and \(h\) guaranteeing the existence of two different solutions to (1), (2) are presented. The proofs are based on the fixed-point theorem on the cone.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00016].