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Sign-changing solutions to singular second-order boundary value problems
We consider elliptic boundary value problems of the form $u''+p(x)|u|^{-\gamma}{{\rm sign}\:} u=0$ and $\Delta u + p(x)|u|^{-\gamma}{{\rm sign}\:} u=0$ for $\gamma>1$ and $p>0$ on intervals in ${\mathbb {R}}$ and bounded domains in ${\mathbb {R}}^n$. Prescribed vanishing Dirichlet boundary data and the concept of sign-changing solutions make the problem singular both …