Positive solutions of a second order Neumann problems with derivative terms

Abstract:

This paper consider the following second-order ~Newmann~ problem with derivative terms $$ \left\{\begin{array}{ll} u''(t)+ku(t)=f(t,u(t),u'(t)),\quad t\in (0,1),\\[2ex] u'(0)=u'(1)=0, \\[2ex] \end{array}. \right.\eqno $$ where~$0