linear versus non-linear integral equations - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T21:47:05Z http://mathoverflow.net/feeds/question/67785 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/67785/linear-versus-non-linear-integral-equations linear versus non-linear integral equations silmaril89 2011-06-14T17:54:14Z 2011-06-14T19:24:17Z <p>I'm having trouble solving an integral equation. It appears to me to be a homogenous fredholm equation of the second kind. However, I'm being told that this can't be a fredholm equation, because it is non-linear. Could someone help me in trying to figure out how to classify an integral equation as linear or non-linear. Also, I'll post the equation I need to solve below, and it would be great if anyone could also give me some tips on how to try and solve it. Thank you to all who reply.</p> <p>The equation is</p> <p>$\phi(x) = (x^2 - x)\int\limits_0^1 \mathrm{d}y \frac{\phi(y)}{(y-x)^2}$</p> <p>Also, is this by chance related to an eigenvalue problem? I know that might sound like a strange question, but I've seen some people treating these as eigenvalue equations.</p> <p>By the way, I want to solve the equation for $\phi(x)$</p> http://mathoverflow.net/questions/67785/linear-versus-non-linear-integral-equations/67787#67787 Answer by Michael Renardy for linear versus non-linear integral equations Michael Renardy 2011-06-14T18:04:09Z 2011-06-14T18:04:09Z <p>The integral diverges unless $\phi(x)=0$. Now look at what happens when you plug $\phi=0$ into the equation. By the way, the equation is linear.</p>