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EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR A HARMONIC EQUATION WITH CRITICAL NONLINEARITY
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作者 kamal ould bouh 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1305-1316,共12页
This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+((n-2)/2)u =((n-2)/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is... This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+((n-2)/2)u =((n-2)/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;). 展开更多
关键词 variational problem critical points harmonic equation mean curvature critical exponent
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