Positive solutions for nonlinear differential equations with periodic boundary conditions (Q2784666)

The subject is the following boundary value problem NEWLINE\[NEWLINE-(p(x)y')' + q(x)y=f(x,y), \quad 0\leq x \leq \omega,\qquad y(0)=y(\omega), \quad y^{[1]}(0)=y^{[1]}(\omega),NEWLINE\]NEWLINE where \(y^{[1]}(x):=p(x)y'(x)\) is a quasi-derivative of \(y(x)\), \(p(x)\) and \(q(x)\) are real-valued measurable functions on \([0,\omega]\) and \(p(x)>0\), \(q(x)\geq 0\), \(q(x)\neq 0\) almost everywhere with \(\int_0^\omega \frac{dx}{p(x)}<\infty\), \(\int_0^\infty q(x) dx<\infty\). NEWLINENEWLINENEWLINEThe existence of positive solutions is proved and upper and lower bounds for these solutions are presented.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00016].