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May 15th, 2017, 06:28 AM  #1 
Member Joined: Dec 2016 From:  Posts: 62 Thanks: 10  Differential equation with delta function
Hi there, I was just trying to solve a differential equation of the following form: \begin{eqnarray} \partial_{x}f(x)\partial_{x}f(x)=\tau \delta(x)(g(x)f(x)  h(x)f(x)) \end{eqnarray} I think the difficult part here is how to treat the delta function on the right handsize, since the equation itself is badly defined there. I just approached taking the following limits $x\to +\varepsilon$ and $x\to \varepsilon$, and integrating the equation between $[\varepsilon,+\epsilon]$, however I know now this doesnt provide a correct answer, is there a general procedure to deal with such differential equations? Thanks! 

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delta, differential, equation, function 
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