Exact multiplicity result for the perturbed scalar curvature problem in <IMG BORDER="0" SRC="/proc/2007-135-01/S0002-9939-06-08644-8/gif-title0/img1.gif" > <IMG BORDER="0" SRC="/proc/2007-135-01/S0002-9939-06-08644-8/gif-title0/img2.gif" >期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Exact multiplicity result for the perturbed scalar curvature problem in

Authors:	S Prashanth

Institution:	TIFR Centre, Indian Institute of Science Campus, P.B. No. 1234, Bangalore - 560 012, India

Abstract:	Let $D^{1,2} (\mathbb{R}^N)$ denote the closure of $C_0^\infty (\mathbb{R}^N)$ in the norm $\Vert u\Vert _{D^{1,2} (\mathbb{R}^N)}^2 = \int\limits_{\mathbb{R}^N} \vert\nabla u\vert^2.$ Let $N \geq 3$ and define the constants $\alpha_N = N (N-2)$ and $C_N = (N (N-2))^{\frac{N-2}{4}}.$ Let $K \in C^2 (\mathbb{R}^N).$ We consider the following problem for $\varepsilon \geq 0:$ $\displaystyle (P_\varepsilon)\qquad\qquad\quad \left\{\begin{array}{llll} \mbox... ...array}\right\} \mbox{ in } \mathbb{R}^N. \end{array} \right. \qquad\quad\qquad$ We show an exact multiplicity result for $(P_\varepsilon)$ for all small $\varepsilon >0$ .

Keywords:	Yamabe problem exact multiplicity scalar curvature

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