Abstract
We present some recent existence and uniqueness results for elliptic boundary value problems involving singular nonlinearities that generalize the Lane‐Emden‐Fowler equation. The following types of problems are considered: (i) singular problems with sublinear nonlinearity and two parameters; (ii) combined effects of asymptotically linear and singular nonlinearities in bifurcation problems; (iii) bifurcation for a class of singular elliptic problems with subquadratic convection term. In some concrete situations we also establish the asymptotic behavior of the solution around the bifurcation point. Our approach relies on maximum principle combined with various techniques for elliptic equations.
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