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Faisceaux maximaux de fonctions associées à un opérateur elliptique du second ordre

Denis Feyel, A. de La Pradelle (1976)

Annales de l'institut Fourier

Soit $F$ le faisceau des sursolutions variationnelles d’un opérateur différentiel elliptique du second ordre à coefficients $L_{loc}^{\infty}$ . Soit $\hat{F}$ le faisceau des régularitées essentielles inférieures des éléments de $F$ . On démontre que $\hat{F}$ est contenu dans un seul préfaisceau $F^{*}$ maximal de cônes convexes de fonctions s.c.i. $> - \infty$ vérifiant le principe du minimum sur une base d’ouverts suffisamment petits. On démontre que $F^{*}$ possède toutes les bonnes propriétés d’une théorie locale du potentiel.

Fatou theorems for some nonlinear elliptic equations.

Eugene Fabes, Nicola Garofalo, Santiago Marin Malave, Sandro Salsa (1988)

Revista Matemática Iberoamericana

Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption.

X.-Y. Chen, Hiroshi Matano, M. Mimura (1995)

Journal für die reine und angewandte Mathematik

Finite-Time Blow-Up for Solutions of Nonlinear Wave Equations.

Robert T. Glassey (1981)

Mathematische Zeitschrift

Fite and Kamenev type oscillation criteria for second order elliptic equations

Zhiting Xu (2007)

Annales Polonici Mathematici

Fite and Kamenev type oscillation criteria for the second order nonlinear damped elliptic differential equation $\sum_{i, j = 1}^{N} D_{i} [a_{i j} (x) D_{j} y] + \sum_{i = 1}^{N} b_{i} (x) D_{i} y + p (x) f (y) = 0$ are obtained. Our results are extensions of those for ordinary differential equations and improve some known oscillation criteria in the literature. Several examples are given to show the significance of the results.

Forced oscillation of certain hyperbolic equations with continuous distributed deviating arguments

Satoshi Tanaka, Norio Yoshida (2005)

Annales Polonici Mathematici

Certain hyperbolic equations with continuous distributed deviating arguments are studied, and sufficient conditions are obtained for every solution of some boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi-dimensional oscillation problems to one-dimensional oscillation problems for functional differential inequalities by using some integral means of solutions.