摘要
We study ordering properties of positive solutions u for the one-dimensional φ-Laplacian quasilinear Dirichlet problem (Formula presented) where γ, L > 0 are two parameters. Assume that φ (Formula presented) C(-k, k) (Formula presented) C <sup>2</sup> ((-k, 0) U (0,k)) is odd for some positive k < ∞, and φ'(t) > 0 for all t (Formula presented) (-k, 0) U (0, k) and f (Formula presented) C[0, n), f (0) > 0, f (u) > 0 on (0, n) for some positive n < ∞, where either n = ∞, or n < ∞ with lim (Formula presented) f (u) = ∞ or lim (Formula presented) f(u) = 0. Some applications are given, including f (u) = u <sup>p</sup> (p > 0), u <sup>p</sup> + u <sup>q</sup> (0 < p < q < ∞), (Formula presented) (p > 0), exp(u), exp ((Formula presented)) (a > 0), and (Formula presented) Keywords: prescribed mean curvature problem; m-Laplacian problem; (m, n)-Laplacian problem; positive solution; bifurcation diagram; ordering property