How does one find eigenvalues $\lambda$ of the following problem? $$ \frac{\mathrm{d}^2 u}{\mathrm{d}x^2} = \lambda \left( -u + u^2 \right), $$ $$ u(0) = u(1) = 0. $$ Can this problem be tackled easily by some software? I have looked into Mathematica but its DEigensystem method is unfortunately taylored for the right hand side of the form $\lambda u$ only.
2026-03-27 13:07:33.1774616853
Nonlinear ODE eigenvalue problem
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A satisfactory answer (to me) appeared on Mathematica StackExchange:
https://mathematica.stackexchange.com/questions/174346/nonlinear-ode-eigenvalue-problem