Abstract
We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (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 sub-quadratic convection term. In some concrete situations we also establish the asymptotic behavior of the solution around the bifurcation point. Our analysis relies on the maximum principle for elliptic equations combined with adequate estimates.
A mon Maître, avec reconnaissance
Partially supported by a research grant with the Romanian Academy and by the CNCSIS grant No. 308 (Nonlinearities and Singularities in Mathematical Physics).
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Rădulescu, V. (2005). Bifurcation and Asymptotics for Elliptic Problems with Singular Nonlinearity. In: Bandle, C., et al. Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 63. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7384-9_38
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DOI: https://doi.org/10.1007/3-7643-7384-9_38
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