Publication at Faculty of Mathematics and Physics |
2011
Abstract
We are concerned with the uniqueness problem for solutions to the second order ODE of the form $x''+f(x,t)=0$, under the sole assumption that $f$ is non-decreasing with respect to $x$, for each $t$ fixed. We show that there is non-uniqueness in general; on the other hand, several types of reasonable additional assumptions yield the problem uniquely solvable.