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Question: 7 consider the problem uquot z u x f...

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7. Consider the problem u (z) + u, (x) f (x) , 0 〈 x 〈 1 = with f a given function (a) Is there one and only one solution i.e is any solution necessarily unique? Explain. (Hint: Take the difference w of any two so- lutions and solve the resulting boundary value problem for the difference w to show that any solution u cannot be unique.) (b) Does a solution necessarily exist or or is there a condition that f (x) must satisfy for existence of solution? Explain. (Hint: In- tegrate the ODE from 0 to l and derive a condition which the function f must satisfy.)

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