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A uniqueness theorem (or its proof) is, at least within the mathematics of differential equations, often combined with an existence theorem (or its proof) to a combined existence and uniqueness theorem (e.g., existence and uniqueness of solution to first-order differential equations with boundary condition). [3]
A standard proof relies on transforming the differential equation into an integral equation, then applying the Banach fixed-point theorem to prove the existence of a solution, and then applying Grönwall's lemma to prove the uniqueness of the solution.
which completes the proof that 3 is the unique solution of + =. In general, both existence (there exists at least one object) and uniqueness (there exists at most one object) must be proven, in order to conclude that there exists exactly one object satisfying a said condition.
This theorem is about the existence of solutions to a system of m differential equations in n dimensions when the coefficients are analytic functions. The theorem and its proof are valid for analytic functions of either real or complex variables. Let K denote either the fields of real or complex numbers, and let V = K m and W = K n.
The state’s unemployment agency potentially overpaid an estimated $55 billion in recent years to people who may not have been eligible for jobless benefits, a California state audit has found.
The Peano existence theorem however proves that even for f merely continuous, solutions are guaranteed to exist locally in time; the problem is that there is no guarantee of uniqueness. The result may be found in Coddington & Levinson (1955, Theorem 1.3) or Robinson (2001, Theorem 2.6).
California’s unemployment remains the highest state rate in the nation. New data from the state’s Employment Development Department put the April rate at 5.3% for the third consecutive month.
It’s a repeat of his previous measure, which Newsom declined to sign because California’s unemployment insurance financing structure is in need of revisions and its trust fund owes more than ...