数学学报 1956, 6(2) 250-262 DOI:   cnki:ISSN:0583-1431.0.1956-02-009   ISSN: 0583-1431 CN: 11-2038/O1

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董光昌
查甫雷金方程的唯一性定理(Ⅱ)
董光昌
浙江大學
摘要: <正> 考虑下列混合型议程的唯一性问题 K(y)u_(xx)+u_(yy)=0 (K(0)=0;当y≠0时,■(1) 所考慮的區域D由三條曲綫圍成.其一是雙曲區域中由原點引出的特徵綫Γ_1,它滿足下面方程
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MSC2000 唯一性定理:9925,解的唯一性:871,格林公式:505,定理1:429,混合型方程:320,定理2:259,增加函数:215,椭圆:181
UNIQUENESS THEOREM FOR CHAPLYGIN’S PROBLEM(Ⅱ)
TONG KWONG-CHONG(Chekiang University)
Abstract: In this paper the uniqueness problem of the Chaplygin's equation K(y) u_(xx)+u_(yy)=0(K(0)=0; dK/dy > 0 for y ≠ 0) is considered. The domain D is bounded by three curves showing in the figure, where Γ_1 and Γ_2 are characteristics define by the equation dx~2+Kdy~2=0, Γ_3 is a continuous curve. Let the ordinate of P be yo and let 1+2 (K/K_y)_y=f(y). Let y_1=0 if f(y)≥0 for all yo≤y< 0, otherwise let y_1 be the upper bound of values y in the interval yo≤y<0 satisfying f(y)< 0.Theorem. If y_1<0 and the following relation holds: and if u is a quasi—regular solution which vanishes on Γ_2 +Γ_3 then u=0 in D.This result is a little better than a result of.The method of proof of the theorem is to the sum of the energy integral + cu_y) (Ku_(xx) + u_(yy) dx dy = 0 and the zero integral + ∮ [u~2 (q dx — p dy) + d(ru~2)] = 0 for suitable choice of a, b, c, p, q, r.
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收稿日期 1955-05-24 修回日期 1900-01-01 网络版发布日期  
DOI: cnki:ISSN:0583-1431.0.1956-02-009
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