Unique Solvability of a Functional-Differential Equation with Orthotropic Contractions in Weighted Spaces

被引：5

作者：

Rossovskii, L. E. ^{[1
]}

Tasevich, A. L. ^{[1
]}

机构：

[1] Peoples Friendship Univ Russia, Moscow 117198, Russia

来源：

DIFFERENTIAL EQUATIONS | 2017年 / 53卷 / 12期

关键词：

D O I：

10.1134/S0012266117120102

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the solvability of a new class of functional-differential equations with transformations of the arguments of the unknown function. The transformations include contractions in one independent variable and dilations in the other. (We refer to such transformations as orthotropic contractions.) Sufficient conditions for the solvability of such equations in weighted spaces are obtained depending on the exponent of the space. We show that the original problem reduces to the study of a certain finite-difference equation in the space L (2)(a"e).

引用

页码：1631 / 1644

页数：14

共 12 条

[1]

Akhmatova A. A., 2012, Tr. Inst. Mat, V20, P14

[2]

[Anonymous], 1998, HDB INTEGRAL EQUATIO

[3]

Antonevich A. B., 1988, LINEINYE FUNKTSIONAL

[4]

Kondratev V.A., 1967, Trans. Moscow Math. Soc, V16, P227

[5]

Plamenevskii B.A., 1986, ALGEBRY PSEVDODIFFER

[6]

Rossovskii LE, 2015, MATH NOTES+, V97, P745, DOI [10.1134/S0001434615050090, 10.4213/mzm10654]

[7]

Rossovskii L. E., 2017, J. Math. Sci, V223, P351, DOI [10.1007/s10958-017-3360-1, DOI 10.1007/S10958-017-3360-1]

[8] Coerciveness of functional-differential equations [J].

Rossovskii, LE .

MATHEMATICAL NOTES, 1996, 59 (1-2) :75-82

[9]

Rudin W., 1973, FUNCTIONAL ANAL, Vsecond

[10]

Skubachevskii A. L., 1997, OPER THEORY ADV APPL, V91

← 1 2 →