Bifurcation and Asymptotics for Elliptic Problems with Singular Nonlinearity

2005/02/07 by Vicenţiu D. Rădulescu, Vicentiu Radulescu, Radulescu, Vicentiu
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0502142

arxiv created 2005/02/07 · openalex publication_date 2005/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 subquadratic convection term. In some concrete situations we also establish the asymptotic behaviour of the solution around the bifurcation point. Our analysis relies on the maximum principle for elliptic equations combined with adequate estimates.

Related

• Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities
• Some Existence Results for a Singular Elliptic Problem via Bifurcation Theory
• Bifurcation and Multiplicity Results for Elliptic Problems with Subcritical Nonlinearity on the Boundary
• A singularity as a break point for the multiplicity of solutions to quasilinear elliptic problems
• Some remarks on singular solutions of nonlinear elliptic equations. I