Existence of two solutions for quasilinear periodic differential equations with discontinuities

Nikolaos S. Papageorgiou; Francesca Papalini

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 4, page 285-296
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Papageorgiou, Nikolaos S., and Papalini, Francesca. "Existence of two solutions for quasilinear periodic differential equations with discontinuities." Archivum Mathematicum 038.4 (2002): 285-296. <http://eudml.org/doc/248927>.

@article{Papageorgiou2002,
abstract = {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.},
author = {Papageorgiou, Nikolaos S., Papalini, Francesca},
journal = {Archivum Mathematicum},
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; one dimensional -Laplacian; maximal monotone operator; pseudomonotone operator; generalized pseudomonotonicity; coercive operator},
language = {eng},
number = {4},
pages = {285-296},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence of two solutions for quasilinear periodic differential equations with discontinuities},
url = {http://eudml.org/doc/248927},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Papageorgiou, Nikolaos S.
AU - Papalini, Francesca
TI - Existence of two solutions for quasilinear periodic differential equations with discontinuities
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 4
SP - 285
EP - 296
AB - 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.
LA - eng
KW - 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; one dimensional -Laplacian; maximal monotone operator; pseudomonotone operator; generalized pseudomonotonicity; coercive operator
UR - http://eudml.org/doc/248927
ER -

References

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