A solution between sub- and supersolutions for semilinear elliptic equations with a nonlocal term in a continuous setting

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A solution between sub- and supersolutions for semilinear elliptic equations with a nonlocal term in a continuous setting

Journal Article (2023)

Author(s)

Philippe Clément (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Guido Sweers (Universität zu Köln)

Research Group

Analysis

Existence Elliptic b.v.p Sub- and supersolutions

DOI related publication

https://doi.org/10.3934/cpaa.2023032 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:b04ba3ed-dd65-4136-afa2-ff624b3f08f6

More Info

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Publication Year

2023

Language

English

Research Group

Analysis

Journal title

Communications on Pure and Applied Analysis

Issue number

4

Volume number

22

Pages (from-to)

1420-1428

Downloads counter

172

Abstract

In the 1987 publication [5] we showed that for second order semilinear elliptic problems a solution exists between a subsolution and a supersolution without using monotone iteration and under minimal assumptions. The alternative is based on a Schauder fixed point argument. Filling some missing details of that paper we noticed that even nonlocal operators are allowed on the right hand side as long as these are quasimonotone. The setting uses ‘weak’-solutions which are continuous on the closure of the domain and solve the equation in distributional sense. As such they differ from the standard weak solutions. We conclude with some examples concerning the setting.