×

zbMATH — the first resource for mathematics

Positive solutions of elliptic equations with discontinuous nonlinearities. (English) Zbl 0891.35038
Summary: An existence theorem of positive solutions to the Dirichlet problem for elliptic equations having nonlinear terms with an uncountable set of discontinuities is established. Some applications to special cases, such as problems with critical Sobolev growth, are also presented. The approach taken is strictly based on set-valued analysis and fixed point arguments.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
PDF BibTeX XML Cite
Full Text: DOI