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Picone’s identity for a Finsler p -Laplacian and comparison of nonlinear elliptic equations

Jaroslav Jaroš (2014)

Mathematica Bohemica

In the paper we present an identity of the Picone type for a class of nonlinear differential operators of the second order involving an arbitrary norm H in n which is continuously differentiable for x 0 and such that H p is strictly convex for some p > 1 . Two important special cases are the p -Laplacian and the so-called pseudo p -Laplacian. The identity is then used to establish a variety of comparison results concerning nonlinear degenerate elliptic equations which involve such operators. We also get criteria...

Positive solutions of inequality with p -Laplacian in exterior domains

Robert Mařík (2002)

Mathematica Bohemica

In the paper the differential inequality Δ p u + B ( x , u ) 0 , where Δ p u = div ( u p - 2 u ) , p > 1 , B ( x , u ) C ( n × , ) is studied. Sufficient conditions on the function B ( x , u ) are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.

Positivity theorem

Jozef Takács (1995)

Acta Mathematica et Informatica Universitatis Ostraviensis

Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien

Alano Ancona (1978)

Annales de l'institut Fourier

L’article étudie le compactifié de Martin d’un domaine lipschitzien Ω relativement à un opérateur elliptique à coefficients hödériens L  ; on étend aux fonctions L -harmoniques et aux fonctions L -harmoniques adjointes sur Ω une estimation de L -Carleson pour le cas L = Δ , puis on établit un “principe de Harnack à la frontière” comparant l’allure à la frontière de fonctions L -harmoniques 0 sur Ω . Conséquences : Q Ω , et normalisée en A 0 Ω  ; un théorème de type Fatou-Doob sur l’existence de limites angulaires.On...

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