Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems

Papageorgiou, Evgenia H., and Papageorgiou, Nikolaos S.. "Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems." Czechoslovak Mathematical Journal 54.2 (2004): 347-371. <http://eudml.org/doc/30865>.

@article{Papageorgiou2004,
abstract = {In this paper we examine nonlinear periodic systems driven by the vectorial $p$-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the “sublinear” problem. For the semilinear problem (i.e. $p = 2$) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the “superlinear” problem. Our work generalizes some recent results of Tang (PAMS 126(1998)).},
author = {Papageorgiou, Evgenia H., Papageorgiou, Nikolaos S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {$p$-Laplacian; nonsmooth critical point theory; Clarke subdifferential; saddle point theorem; periodic solution; Poincare-Wirtinger inequality; Sobolev inequality; nonsmooth Palais-Smale condition; -Laplacian; nonsmooth critical point theory; Clarke subdifferential; saddle point theorem},
language = {eng},
number = {2},
pages = {347-371},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems},
url = {http://eudml.org/doc/30865},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Papageorgiou, Evgenia H.
AU - Papageorgiou, Nikolaos S.
TI - Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 347
EP - 371
AB - In this paper we examine nonlinear periodic systems driven by the vectorial $p$-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the “sublinear” problem. For the semilinear problem (i.e. $p = 2$) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the “superlinear” problem. Our work generalizes some recent results of Tang (PAMS 126(1998)).
LA - eng
KW - $p$-Laplacian; nonsmooth critical point theory; Clarke subdifferential; saddle point theorem; periodic solution; Poincare-Wirtinger inequality; Sobolev inequality; nonsmooth Palais-Smale condition; -Laplacian; nonsmooth critical point theory; Clarke subdifferential; saddle point theorem
UR - http://eudml.org/doc/30865
ER -