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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.
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