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- W2801387310 abstract "Let begin{document} $(M, g)$ end{document} be a smooth compact riemannian manifold of dimension begin{document} $N≥2$ end{document} with constant scalar curvature. We are concerned with the following elliptic problem begin{document}$begin{eqnarray*}-{varepsilon}^2Δ_g u+ u = u^{p-1}, ~~~~u>0, in M.end{eqnarray*}$ end{document} where begin{document} $Δ_g$ end{document} is the Laplace-Beltrami operator on begin{document} $M$ end{document} , begin{document} $p>2$ end{document} if begin{document} $N = 2$ end{document} and begin{document} $2 if begin{document} $N≥3$ end{document} , begin{document} $varepsilon$ end{document} is a small real parameter. We prove that there exist a function begin{document} $Ξ$ end{document} such that if begin{document} $ξ_0$ end{document} is a stable critical point of begin{document} $Ξ(ξ)$ end{document} there exists begin{document} ${varepsilon}_0>0$ end{document} such that for any begin{document} ${varepsilon}∈(0,{varepsilon}_0)$ end{document} , problem (1) has a solution begin{document} $u_{varepsilon}$ end{document} which concentrates near begin{document} $ξ_0$ end{document} as begin{document} ${varepsilon}$ end{document} tends to zero. This result generalizes previous works which handle the case where the scalar curvature function of begin{document} $(M,g)$ end{document} has non-degenerate critical points." @default.
- W2801387310 created "2018-05-17" @default.
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- W2801387310 date "2018-01-01" @default.
- W2801387310 modified "2023-09-26" @default.
- W2801387310 title "On spike solutions for a singularly perturbed problem in a compact riemannian manifold" @default.
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- W2801387310 doi "https://doi.org/10.3934/cpaa.2018098" @default.
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