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A unified characterization of convolution coefficients in nonlocal differential equations
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 18 September 2024, pp. 1-19
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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.
