Existence and Uniqueness theorem and how to use it in an example

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Differential Equations
Existence and Uniqueness theorem and how to use it in an example

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Uniqueness Theorem For Poisson's Equation
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Isn't it that there is a unique solution in around any points expect y>2, not just y =/ 2? since f = 5(y-2)^(3/5) is continuous on [2, inf.)

이찬우-ji

since the functions does't satisfy Lipschitz conditions it means that the solution is not unique but exist since
it is continuous.
Picard's theorem state that: if the function is Lipschitz and continuous i.e solution exist and is unique

idrissakayijuka

I think there is a mistake at minune 8:19. Accordying to the theorem of uniqueness, it can only be used to state that a solution is unique. We can not use it to state that the solution is not unique. Therefore the final statement on minute 8:19 can not be made. But I am not sure, can anyone confirm this?

segoviapatricio

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