Two point boundary value problems for the Sturm-Liouville equation with highly discontinuous nonlinearities
The existence of three solutions for the boundary value problem \[ \begin{cases} -(\overline{p}u')' + \overline{r}u' = \lambda g(u) \;\;\text{in} \;(a,b), \\ u(a)=u(b)=0 \end{cases} \] is established, where \(\overline{p}\), \(\overline{r}\), \(\overline{q} \in L^\infty[a,b]\) and \(g\): \({\mathbb R} \to {\mathbb R}\) is an almost everywhere continuous function. Here, the set of the points of discontinuity of \(g\) may be uncountable but, solutions are actually generalized solutions. The approach is the critical point theory for non-differentiable functions.
scientific article; zbMATH DE number 5910203