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- W4384383304 abstract "<abstract><p>This paper investigates the existence of positive solutions for a nonhomogeneous nonlinear integral equation of the form</p> <p><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{equation} u^{p-1}(x) = int_{Omega} frac{u(y)}{|x-y|^{n-alpha}} d y+int_{Omega} frac{f(y)}{|x-y|^{n-alpha}} d y, x in bar{Omega}nonumber end{equation} $end{document} </tex-math></disp-formula></p> <p>where $ frac{2n}{n+alpha}leq p < 2, $ $ 1 < alpha < n $, $ n > 2, $ $ Omega $ is a bounded domain in $ mathbb R^{n} $. We show that under suitable assumptions on $ f, $ the integral equation admits a positive solution in $ L^{frac{2n}{n+alpha}}left(Omegaright) $. Our method combines the Ekeland variational principle, a blow-up argument and a rescaling argument which allows us to overcome the difficulties arising from the lack of Brezis-Lieb lemma in $ L^{frac{2n}{n+alpha}}(Omega) $.</p></abstract>" @default.
- W4384383304 created "2023-07-15" @default.
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- W4384383304 date "2023-01-01" @default.
- W4384383304 modified "2023-10-16" @default.
- W4384383304 title "Nonhomogeneous nonlinear integral equations on bounded domains" @default.
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- W4384383304 doi "https://doi.org/10.3934/math.20231132" @default.
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