Last Updated：2025/12/03
Sentence
微分方程式の解の一意性を保証するために、教科書は右辺が初期値の近傍で、ある点の近傍に定数Lが存在し、その近傍内の任意の二点について関数値の差の絶対値が点の差の絶対値のL倍以下となるという性質（リプシッツ条件）を満たすことを要求している。
Quizzes for review
To ensure uniqueness of solutions to the differential equation, the textbook requires that the right-hand side satisfy the Lipschitz condition in a neighborhood of the initial value.
See correct answer
To ensure uniqueness of solutions to the differential equation, the textbook requires that the right-hand side satisfy the Lipschitz condition in a neighborhood of the initial value.
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Related words
Lipschitz condition
Noun
(mathematical
analysis)
A
property
which
can
be
said
to
be
held
by
some
point
in
the
domain
of
a
real-valued
function
if
there
exists
a
neighborhood
of
that
point
and
a
certain
constant
such
that
for
any
other
point
in
that
neighborhood,
the
absolute
value
of
the
difference
of
their
function
values
is
less
than
the
product
of
the
constant
and
the
absolute
value
of
the
difference
between
the
two
points.
Japanese Meaning
数学的解析における概念で、ある実数値関数が、特定の点の近傍内で、任意の2点間においてその関数値の差が、ある一定の正の定数と入力値の差の積よりも小さいという性質。すなわち、ある定数 L > 0 と、その点の近傍が存在し、任意の x, y に対して |f(x) - f(y)| ≤ L|x - y| が成立することを指す。
Related Words
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