Abstract:The weak and strong comparison principles (WCP and SCP, respectively) are investigated for quasilinear elliptic boundary value problems with the p-Laplacian in one space dimension, ∆ p (u) def = d dx |u | p−2 u . We treat the "degenerate" case of 2 < p < ∞ and allow also for the nontrivial convection velocity b : [−1, 1] → R in the underlying domain Ω = (−1, 1). We establish the WCP under a rather general, "natural sufficient condition" on the convection velocity, b(x), and the reaction function, ϕ(x, u). Furt… Show more
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