A unified characterization of convolution coefficients in nonlocal differential equations

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。
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来源期刊
CiteScore
3.00
自引率
0.00%
发文量
72
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.
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The structure of finite groups whose elements outside a normal subgroup have prime power orders A unified characterization of convolution coefficients in nonlocal differential equations On a supersonic-sonic patch arising from the two-dimensional Riemann problem of the compressible Euler equations Dual formulation of constrained solutions of the multi-state Choquard equation Duality pairs, phantom maps, and definability in triangulated categories
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