A generalized anti-maximum principle for the periodic one-dimensional p-Laplacian with sign-changing potential

0343853 - MÚ 2011 RIV GB eng J - Journal Article
Cabada, A. - Cid, J.A. - Tvrdý, Milan
A generalized anti-maximum principle for the periodic one-dimensional p-Laplacian with sign-changing potential.
Nonlinear Analysis: Theory, Methods & Applications. Roč. 72, 7-8 (2010), s. 3436-3446. ISSN 0362-546X. E-ISSN 1873-5215
R&D Projects: GA AV ČR IAA100190703
Institutional research plan: CEZ:AV0Z10190503
Keywords : anti-maximum principle * periodic problem * Dirichlet problem * p-Laplacian * singular problem
Subject RIV: BA - General Mathematics
Impact factor: 1.279, year: 2010
http://www.sciencedirect.com/science/article/pii/S0362546X0901253X

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].
Permanent Link: http://hdl.handle.net/11104/0186231