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I try to solve second order PDE:

[itex] \frac{\partial^2 f(x,y)}{\partial x^2}=-a^2f(x,y) [/itex]

[itex] \frac{\partial^2 f(x,y)}{\partial y^2}=-a^2f(x,y) [/itex]

where [itex] a >2[/itex], [itex] f(x,y)[/itex] is a periodic function in x, but has fixed boundaries in y.

Is there a way to solve it? What does the solution look like? Any hints or references are welcome. thanks a lot!

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# Laplacian-like equation

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