Dini Derivatives Sample Clauses

Dini Derivatives. Consider the nonautonomous system y˙ = f (t, y), (2.1) where D ⊂ Rm is a domain and f : R × D → Rm. Let V (t, y) : R × D → R be a continuous function satisfying a local Lipschitz condition for y, uniformly with respect to t. Then we define D+V (t, y) = lim sup V (t + τ, y + τ f (t, y)) − V (t, y) . τ→0+ τ The function D+V is called the upper Dini derivative of V along the trajectory of (2.1). Suppose that for an initial condition y(0) = y0, (2.1) has a solution y(t) defined on an interval [0, η) and let D+V (t, y(t)) be the upper Dini derivative of V (t, y(t)) with respect to t, i.e., D+V (t, y(t)) = lim sup V (t + τ, y(t + τ)) − V (t, y(t)) . τ→0+ τ Let t∗ ∈ [0, η) and put y(t∗) = y∗. Then one has that (see [33]) D+V (t∗, y(t∗)) = D+V (t∗, y∗).
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Dini Derivatives. Consider the nonautonomous system

Related to Dini Derivatives

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  • Technology Discoveries, innovations, Know-How and inventions, whether patentable or not, including computer software, recognized under U.S. law as intellectual creations to which rights of ownership accrue, including, but not limited to, patents, trade secrets, maskworks and copyrights developed under this Agreement.

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