M****i
发帖数: 58 | 1 Consider the following second order linear ODE with mixed boundary condition: f''(t)+a(t)f(t)=0, f'(0)=u, f(1)=0, where u is a fixed real number and a(t) is a fixed continuous function on [0,1]. Is the solution to this equation unique? If so, how to prove it? Thanks! | w**********r
发帖数: 128 | 2 Not necessarily. For example,
( sin t )'' + ( sin t) =0
(sin t)'=0 when t= pi/2 sin pi =0
This example can be modified to give a negative answer to your question. | M****i
发帖数: 58 | 3 Thank you very much for your answer. When a(t) is constant, one has general
solutions but what if a(t) is not a constant? Now I do think that the
solution is not unique and maybe even does't exist. |
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