Solution-Minimal solution that comes arbitrarily close to

Minimal solution that comes arbitrarily close to boundary

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Reference no: EM132166447

Problem need to proof by using Peno therom

Find the Minimal solution with the condition that it is unbounded

1. If f (x, y) is continuous in a domain D the IVP

y' = f(x,Y), y(ξ) = η, with (ξ, n) ∈ D

has a minimal solution that comes arbitrarily close to the boundary of D both to the left and right such that y*(x) ≤ y(x). (Do not assume that f is bounded in D.)

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In the assignment, the question needs to get prove through peno theorem. So, with the help of fundamental theorem of calculus and Picard iteration, we proved the answer.

Reference no: EM132166447

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11/14/2018 10:18:04 PM

Differential Equations/Linear Algebra Extra Credit Assignment Note: The answer to the following problem is to be submitted latest by the class time on Tuesday. Your answer must be well supported with cohesive and logical arguments, complete details and citations, if any, of the theorems from the text. The maximum credit you can get for correct and complete answer is 0.5 x (30 - Test I score)

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Minimal solution that comes arbitrarily close to boundary

Reference no: EM132166447

Reference no: EM132166447

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