Two point boundary value problems for the Sturm-Liouville equation with highly discontinuous nonlinearities
type: Item
instance of: scholarly article
title: Two point boundary value problems for the Sturm-Liouville equation with highly discontinuous nonlinearities
zbMATH Open document ID: 1237.34026
author: Stefania Maria Buccellato
author: Gabriele Bonanno
published in: Taiwanese Journal of Mathematics
publication date: 2011-06-21T00:00:00Z
review text: 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.
reviewed by: Satoshi Tanaka
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 58E50
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5910203
zbMATH Keywords: critical points
zbMATH Keywords: variational methods
zbMATH Keywords: discontinuous nonlinearities
zbMATH Keywords: Sturm-Liouville problem
zbMATH Keywords: multiple solutions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406032
OpenAlex ID: W4256102136
DOI: 10.11650/TWJM/1500406032
description: scientific article; zbMATH DE number 5910203