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April 2nd, 2014, 12:15 AM  #1 
Newbie Joined: Jan 2014 Posts: 1 Thanks: 0  eigenvalue problem
Hello guys, suppose we have an eigenvalue problem together with boundary conditions \begin{array}{ll} 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} \end{array} 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. Thanks 

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