Construction of Domains with All Solutions, and the Existence of Extreme Solutions

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1981 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 18, pages 801-807 (issn: 0036-1429, eissn: 1095-7170,

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Authors: Wildenauer, Peter;

doi: 10.1137/0718054

Construction of Domains with All Solutions, and the Existence of Extreme Solutions

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Abstract

In this paper we construct domains with all solutions of an operator equation $Fu = 0$, and prove the existence of a minimal and maximal solution. For this one requires a suitable growth condition of F and the existence of a solution of $Fu = 0$ in intervals $[\Phi ,\Psi ]$, if $\Phi $ is a subsolrution and $\Psi $ is a supersolution for $Fu = 0$.

Keywords

ordered groups, Equations involving nonlinear operators (general), initial points for iterative procedures, existence of extreme solutions, nonlinear elliptic boundary value problems

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