A unified characterization of convolution coefficients in nonlocal differential equations

IF 1.3 3区数学 Q1 MATHEMATICS

Proceedings of the Royal Society of Edinburgh Section A-Mathematics Pub Date : 2024-09-18 DOI:10.1017/prm.2024.77

Christopher S. Goodrich

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引用次数: 0

Abstract

In loving memory of my beloved miniature dachshund Maddie (16 March 2002 – 16 March 2020). We consider nonlocal differential equations with convolution coefficients of the form

\[{-}M\Big(\big(a*(g\circ |u|)\big)(1)\Big)u''(t)=\lambda f\big(t,u(t)\big),\quad t\in(0,1), \]

in the case in which

$g$

can satisfy very generalized growth conditions; in addition,

$M$

is allowed to be both sign-changing and vanishing. Existence of at least one positive solution to this equation equipped with boundary data is considered. We demonstrate that the nonlocal coefficient

$M$

allows the forcing term

$f$

to be free of almost all assumptions other than continuity.

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非局部微分方程中卷积系数的统一表征

深切缅怀我心爱的迷你腊肠犬麦迪（2002 年 3 月 16 日 - 2020 年 3 月 16 日）。我们考虑非局部微分方程的卷积系数形式为 \[{-}M\Big(\big(a*(g\circ |u|)\big)(1)\Big)u''(t)=\lambda f\big(t,u(t)\big),\quad t\in(0,1), \]，在这种情况下，$g$可以满足非常广义的增长条件；此外，允许 $M$ 既是符号变化的又是消失的。我们考虑了该方程至少有一个正解的存在性，并给出了边界数据。我们证明，非局部系数 $M$ 可以使强制项 $f$ 不受连续性以外的几乎所有假设的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the Royal Society of Edinburgh Section A-Mathematics 数学-数学

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.