Squeeze theorem

Squeeze theorem

Functions of Several Variables

Published in John Srdjan Petrovic, Advanced Calculus, 2020

When f is a function of one variable and the task at hand is to prove that limx→af (x) = L, the Squeeze Theorem (Theorem 3.6.15) can be a very powerful tool. The same is true when f depends on more than one variable.

Prescribed-time stabilisation design for a class of nonlinear systems with state constraints

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Journal Information

Published in International Journal of Systems Science, 2023

Siqi Wang, Ruicheng Ma

(ii) We are going to show first that is . When , we have By Squeeze Theorem and from (41), we obtain that Then, we can further obtain that from (43): By (44), when i = 1, we have . Thus, we know that is continuous at and then the of (4) is continuous at .

Traveling waves in an SEIR epidemic model with a general nonlinear incidence rate

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Published in Applicable Analysis, 2020

Xin Wu, Baochuan Tian, Rong Yuan

Next, we will verify the asymptotic boundary conditions (15). Note that and . It follows from the squeeze theorem that and as . Recall the integral form of : By the L'Hospital rule, it holds that Applying the L'Hospital rule to the maps and , it is easy to show that and . From (43), we obtain Using the L'Hospital rule again, we get Finally, it follows from (20)–(22) that , and .

Traveling waves for a nonlocal dispersal SIR model with renewal and spatio-temporal delay

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Published in Applicable Analysis, 2023

Yun-Rui Yang, Yang Yang, Zhu-Yan Ma

Since satisfies (35), the construction of implies that It is not difficult to testify Hence, the solution converges to as and , by the Squeeze theorem.

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