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- W3208275754 abstract "Given a smooth bounded domain $Omega$ in $mathbb{R}^2$, we study the following anisotropic Neumann problem $$ begin{cases} -nabla(a(x)nabla u)+a(x)u=lambda a(x) u^{p-1}e^{u^p},,,,, u>0,,,,, textrm{in},,,,, Omega,[2mm] frac{partial u}{partialnu}=0,, qquadquadqquadqquadqquadqquadqquad ,qquadquad, textrm{on},,, partialOmega, end{cases} $$ where $lambda>0$ is a small parameter, $0<p<2$, $a(x)$ is a positive smooth function over $overline{Omega}$ and $nu$ denotes the outer unit normal vector to $partialOmega$. Under suitable assumptions on anisotropic coefficient $a(x)$, we construct solutions of this problem with arbitrarily many mixed interior and boundary bubbles which concentrate at totally different strict local maximum or minimal boundary points of $a(x)$ restricted to $partialOmega$, or accumulate to the same strict local maximum boundary point of $a(x)$ over $overline{Omega}$ as $lambdarightarrow0$." @default.
- W3208275754 created "2021-11-08" @default.
- W3208275754 creator A5039253932 @default.
- W3208275754 date "2021-10-25" @default.
- W3208275754 modified "2023-09-27" @default.
- W3208275754 title "Boundary concentration phenomena for an anisotropic Neumann problem in $mathbb{R}^2$" @default.
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- W3208275754 doi "https://doi.org/10.48550/arxiv.2110.13378" @default.
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