Geodesic
Existence of solutions for discontinuous functional equations and elliptic boundary-value problems
Electronic journal of differential equations, Tome 2002 (2002)
We prove existence results for discontinuous functional equations in general $L^p$-spaces and apply these results to the solvability of implicit and explicit elliptic boundary-value problems involving discontinuous nonlinearities. The main tool in the proof is a fixed point result in lattice-ordered Banach spaces proved by the second author.
Classification : 35J65, 35R05, 35R10
Keywords: functional equations, elliptic boundary-value problems, discontinuous nonlinearities 
@article{EJDE_2002__2002__a292,
     author = {Carl,  Siegfried and Heikkil\"a,  Seppo},
     title = {Existence of solutions for discontinuous functional equations and elliptic boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1001.35044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a292/}
}
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%A Heikkilä,  Seppo
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Carl,  Siegfried; Heikkilä,  Seppo. Existence of solutions for discontinuous functional equations and elliptic boundary-value problems. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a292/