On the existence of positive solutions of nonlinear differential equations of high order (Q5929079)

Here, the authors prove, that the infinitely many solutions result by Zhao is applicable to the following nonlinear differential equation NEWLINE\[NEWLINEL^2= L(Lu)= -f(.,u)\quad\text{in }(0,\omega),NEWLINE\]NEWLINE with \(\omega\in (0,\infty]\), \(f\) a measurable function on \((0,\omega)\times (0,\infty)\) dominated by a regular function, and \(L\) the differential operator of second order defined on \((0,\omega)\) by \(Lu={1\over A} (Au')'\), where \(A\) is a continuous function on \([0,\omega)\), infinitely differentiable and positive on \((0,\omega)\).