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

@inproceedings{Cabada2009AGA,
title={A generalized anti-maximum principle for the periodic one dimensional p-Laplacian with sign changing potential},
author={Alberto Cabada and Jos{\'e} {\'A}ngel Cid and Milan Tvrd{\'y}},
year={2009}
}

It is known that the antimaximum principle holds for the quasilinear periodic problem (|u′|p−2u′)′ + μ(t) (|u|p−2u) = h(t), u(0) = u(T ), u′(0) = u′(T ), if μ ≥ 0 in [0, T ] and 0 < ‖μ‖∞ ≤ (πp/T ) , where πp = 2 (p− 1) ∫ 1 0 (1− sp)−1/p ds, or p = 2 and 0 < ‖μ‖α ≤ inf { ‖u‖2 ‖u‖α : u ∈ W 1,2 0 [0, T ] \ {0} } for some α, 1≤α≤∞. In this paper we give sharp conditions on the Lα -norm of the potential μ(t) in order to ensure the validity of the antimaximum principle even in case that μ(t) can… CONTINUE READING