説明
<jats:title>Abstract</jats:title><jats:p>We consider the following mean field equations: <jats:disp-formula> </jats:disp-formula> where <jats:italic>M</jats:italic> is a compact Riemann surface with volume 1, <jats:italic>h</jats:italic> is a positive continuous function on <jats:italic>M</jats:italic>, ρ is a real number, <jats:disp-formula> </jats:disp-formula> and where Ω is a bounded smooth domain, <jats:italic>h</jats:italic> is a <jats:italic>C</jats:italic><jats:sup>1</jats:sup> positive function on Ω, and ρ ∈ ℝ. Based on our previous analytic work [14], we prove, among other things, that the degree‐counting formula for (<jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#eqn1">0.1</jats:ext-link>) is given by (<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/tex2gif-stack-1.gif" xlink:title="urn:x-wiley:00103640:media:CPA10107:tex2gif-stack-1" />) for ρ ∈ (8<jats:italic>m</jats:italic>π, 8(<jats:italic>m</jats:italic> + 1)π). © 2003 Wiley Periodicals, Inc.</jats:p>
収録刊行物
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- Communications on Pure and Applied Mathematics
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Communications on Pure and Applied Mathematics 56 (12), 1667-1727, 2003-09-29
Wiley