I'm struggling with solving the following equation for $\Delta(\omega)$, $$ \Delta(\omega)=\frac{1}{2}\int_{-\infty}^{\infty}\frac{d\Omega}{\sqrt{\Omega^2+\Delta^2(\Omega)}}\left(\frac{\omega\Delta(\Omega)-\Omega\Delta(\omega)}{\omega}\right)\frac{1}{|\omega-\Omega|^{1/3}} $$ the only information I have about $\Delta(\omega)$ is its value at $\omega=0$, $\Delta(0)=8.14$, I think I should be able to obtain some approximate solution by some iterative method, however I've no idea how to go about it for a equation of this form.
2026-03-26 21:13:31.1774559611
Solving a non-linear, improper integral equation
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