EXISTENCE AND UNIQUENESS OF A LOCAL SOLUTION FOR x′ = f(t, x) USING INVERSE FUNCTIONS

被引：0

作者：

Hoag, Jeffrey T. ^{[1
]}

机构：

[1] Providence Coll, Dept Math, Providence, RI 02918 USA

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年

关键词：

Existence; uniqueness; ordinary differential equation;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A condition on the function f is given such that the scalar ordinary differential equation x' - f(t, x) with initial condition x(t(0)) - x(0) has a unique solution in a neighborhood of t(0). An example illustrates that this result can be used when other theorems which put conditions on the difference f(t, x) - f(t, y) do not apply.

引用

页数：3

共 5 条

[1] Agarwal R. P., 1993, Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations
[2] [Anonymous], 1898, Monatshefte Math. Phys.
[3] A UNIQUENESS THEOREM FOR Y'=F(X,Y) USING A CERTAIN FACTORIZATION OF F
BOWNDS, JM
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1970, 7 (02) : 227 - &
[4] Nagumo M., 1926, Jpn. J. Math., V3, P107
[5] An adequate condition for the unity of solutions of first order differential equations
Perron, O
[J]. MATHEMATISCHE ZEITSCHRIFT, 1928, 28 : 216 - 219

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