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A generalized anti-maximum principle for the periodic one-dimensional p-Laplacian with sign-changing potential
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SYSNO ASEP 0343853 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A generalized anti-maximum principle for the periodic one-dimensional p-Laplacian with sign-changing potential Author(s) Cabada, A. (ES)
Cid, J.A. (ES)
Tvrdý, Milan (MU-W) RID, ORCID, SAISource Title Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 72, 7-8 (2010), s. 3436-3446Number of pages 11 s. Language eng - English Country GB - United Kingdom Keywords anti-maximum principle ; periodic problem ; Dirichlet problem ; p-Laplacian ; singular problem Subject RIV BA - General Mathematics R&D Projects IAA100190703 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000275265700018 EID SCOPUS 75449113395 DOI 10.1016/j.na.2009.12.028 Annotation It is known that the anti-maximum principle holds for the quasilinear periodic problem (vertical bar u'vertical bar(p-2)u')' + mu(t) (vertical bar u vertical bar(p-2)u) = h(t), u(0) = u(T), u'(0) = u'(T), if mu >= 0 in [0, T] and 0 < parallel to mu parallel to(infinity) <= (pi(p)/T)(p), where pi(p) = 2(p - 1)(1/p) integral(1)(0) (1 - s(p))(-1/p) ds, or p = 2 and 0 < parallel to mu parallel to(alpha) <= inf {parallel to u'parallel to(2)(2)/parallel to u parallel to(2)(alpha) : u is an element of W-0(1,2)[0, T] backslash {0}} for some alpha, 1 <= alpha <= infinity. In this paper we give sharp conditions on the L-alpha-norm of the potential mu(t) in order to ensure the validity of the anti-maximum principle even in the case where mu(t) can change its sign in [0, T]. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2011
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