By E. Grosswald

ISBN-10: 3540091041

ISBN-13: 9783540091042

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It follows that (A3)–(ii) is satisfied for the p–Laplacian with ν = max{1, σ02−p }. Also (A3)–(i) is satisfied for the p–Laplacian with c = |p − 2| and for the mean curvature operator with c = 1, etc. 1. Let conditions (A1) , (A2) , (A3) and (B1) hold. 6) is satisfied. 2. Let conditions (A1) and (A2) hold, let g ij = g ij (x) be independent of u and of class C 2 (Ω), and assume (B1) applies with Φ(|ξ|) replaced by Φ(|ξ|g ). 6) is satisfied. 1. 7) due to the presence of the metric [g ij ], and with a slight (but not trivial) difference in the definition of the comparison function v = v(r).

In [25] a version of the strong maximum principle at infinity, the so–called Omori–Yau principle, has recently been given for singular elliptic inequalities including the p–Laplacian case as well as the mean curvature operator, and for smooth, connected, non–compact, complete Riemannian manifolds M. 10. 1. 2) ˆ v, Dv) ≥ 0, ˆ v, Dv)} − B(x, div{A(x, v ≥ 0, in a bounded domain Ω ⊂ Rn . Let the vector function ˆ z, ξ) : Ω × R × Rn → Rn A(x, be continuous in Ω × R × Rn and continuously differentiable with respect to z and ξ for all z and for ξ = 0.

Fennicae, Ser. A, I. Mathematica Dissertationes Number 21, (1978). , Elementare Bemerkungen u ˝ber die L˝ osungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, Sitzungsberichte Preussiche Akademie Wissenschaften, Berlin, 1927, 147– 152. [21] Kawhol, B. and N. Kutev, Strong maximum principle for semicontinuous viscosity solutions to nonlinear partial differential equations, Arch. , 70 (1998), 470–478. , A strong maximum principle for weakly L–subharmonic functions, J.

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Bessel Polynomials by E. Grosswald


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