Oscillation Criteria for Semilinear Equations in General Domains

Author:

Allegretto W.

Abstract

Oscillation theory for nonlinear ordinary differential equations has been extensively developed in recent years by several authors. We refer the reader to the recent paper by Noussair and Swanson, [2], where an extensive bibliography may be found. The situation is somewhat different for the case of second order partial differential equations, an area which has recently been virtually untouched, except for the establishment of criteria which depend on a comparison with suitable linear equations and therefore are essentially linear in nature. A bibliography of such results may also be found in [2]. Of a more general nature have been the paper by the author [1], and the more recent work of Noussair and Swanson, [2]. Although the methods employed and the equations considered in [1] and [2] are different, both papers obtained results only for a class of exterior domains of Rn, of which the typical example is the complement of a bounded sphere.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Oscillation Properties of Solutions of Second Order Elliptic Equations;SIAM Journal on Mathematical Analysis;1983-07

2. Oscillation criteria for semilinear metaharmonic equations in exterior domains;Archive for Rational Mechanics and Analysis;1980-03

3. Sturmian theory of second-order elliptic differential equations and inequalities;Journal of Mathematical Analysis and Applications;1979-12

4. Oscillation of semilinear ultrahyperbolic differential operators;Annali di Matematica Pura ed Applicata;1979-12

5. Oscillation theorems for semilinear elliptic differential operators;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;1978

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