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May 15th, 2017, 06:28 AM   #1
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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 hand-size, 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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