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April 2nd, 2014, 12:15 AM   #1
Joined: Jan 2014

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eigenvalue problem

Hello guys, suppose we have an eigenvalue problem together with boundary conditions

u'' + λu = 0, \quad x \in (0,\pi) \\
u(0)=0 \quad \\
\left( \int_0^\pi \! {(u^+)}^2 \, \mathrm{d}x \right)^{\frac{1}{2}} = \left( \int_0^\pi \! {(u^-)}^4 \, \mathrm{d}x \right)^\frac {1}{4}


where $ u^+$ ,$ u^-$ is positive, negative part of function respectively.
I'm having troubles with case when λ> 0. Is there any way how to simplify or express these parts of function ? I've tried some (analytic) brute force methods, tried to simplify that first but still no valuable result.
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