Positive solutions of periodic boundary value problems for second-order differential equations with the nonlinearity dependent on the derivative (Q499998)

The authors are concerned with the existence of positive solutions for the periodic boundary value problem \[ \begin{aligned} -(pu')'+&qu=h(t)f(u,u'),\quad 0<t<\omega\\ &u(0)=u(\omega),\;u'(0)=u'(\omega), \end{aligned} \] where \(h: [0,\omega]\longrightarrow[0,+\infty)\) and \(f: [0,+\infty)\times\mathbb{R}\longrightarrow[0,+\infty)\) are continuous functions. \(q\) is nonnegative and \(p\) is a \(C^1\) positive function. The authors prove the existence of positive solutions under sublinearity-like grow conditions on \(f\) with respect to \(| u|+| u'|\). They apply Mawhin's coincidence degree theorem.