Geodesic
Existence of two solutions for quasilinear periodic differential equations with discontinuities
Archivum mathematicum, Tome 38 (2002) no. 4, pp. 285-296.

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In this paper we examine a quasilinear periodic problem driven by the one- dimensional $p$-Laplacian and with discontinuous forcing term $f$. By filling in the gaps at the discontinuity points of $f$ we pass to a multivalued periodic problem. For this second order nonlinear periodic differential inclusion, using variational arguments, techniques from the theory of nonlinear operators of monotone type and the method of upper and lower solutions, we prove the existence of at least two non trivial solutions, one positive, the other negative.
Classification : 34A36, 34B15, 34C25
Keywords: one dimensional $p$-Laplacian; maximal monotone operator; pseudomonotone operator; generalized pseudomonotonicity; coercive operator; first nonzero eigenvalue; upper solution; lower solution; truncation map; penalty function; multiplicity result 
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     author = {Papageorgiou, Nikolaos S. and Papalini, Francesca},
     title = {Existence of two solutions for quasilinear periodic differential equations with discontinuities},
     journal = {Archivum mathematicum},
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     publisher = {mathdoc},
     volume = {38},
     number = {4},
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     mrnumber = {1942658},
     zbl = {1090.34013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2002__38_4_a4/}
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Papageorgiou, Nikolaos S.; Papalini, Francesca. Existence of two solutions for quasilinear periodic differential equations with discontinuities. Archivum mathematicum, Tome 38 (2002) no. 4, pp. 285-296. http://geodesic.mathdoc.fr/item/ARM_2002__38_4_a4/