SOLVABILITY OF INHOMOGENEOUS BOUNDARY-VALUE PROBLEMS FOR FOURTH-ORDER DIFFERENTIAL EQUATIONS

被引：1
作者：
Buryachenko, K. O. [1 ]
机构：
[1] Donetsk Natl Univ, Donetsk, Ukraine
来源：
UKRAINIAN MATHEMATICAL JOURNAL | 2012年 / 63卷 / 08期
关键词：
Sobolev Space; Dirichlet Problem; Constant Complex; Minimum Operator; Partial Differential Operator;
D O I：
10.1007/s11253-012-0570-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a Cauchy-type boundary-value problem, a problem with three boundary conditions, and the Dirichlet problem for a general typeless fourth-order differential equation with constant complex coefficients and nonzero right-hand side in a bounded domain Omega subset of R-2 with smooth boundary. By the method of the Green formula, the theory of extensions of differential operators, and the theory of L-traces (i.e., traces associated with the differential operation L); we establish necessary and sufficient (for elliptic operators) conditions of the solvability of each of these problems in the space H-m(Omega), m >= 4:
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页码：1165 / 1175
页数：11
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