Multi-parameter bifurcation and asymptotics for the singular Lane–Emden–Fowler equation with a convection term

Multiparameter bifurcation and asymptotics for the singular Lane-Emden-Fowler equation with convection term

We establish some bifurcation results for the boundary value problem −∆u = g(u) + λ|∇u| + μf(x, u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in R , λ, μ ≥ 0, 0 < p ≤ 2, f is nondecreasing with respect to the second variable, and g is unbounded around the origin. The asymptotic behaviour of the solution around the bifurcation point is also established, provided g(u) behav...

Bifurcation and Asymptotics for Elliptic Problems with Singular Nonlinearity

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) bifurca...

Asymptotics of Blowup for a Convection-diffusion Equation with Conservation

This paper deals with a parabolic partial differential equation that incorporates diffusion and convection terms and that previously has been shown to have solutions that become unbounded at a single point in finite time. The results presented here describe the limiting behavior of the solution in a neighborhood of the blowup point, as well as the asymptotic growth rate as the blowup time is ap...

Multi-Parameter Bifurcation and Applications

where λ, ε > 0, f is a nonlinear function, and Ω is a smooth bounded domain in Rn. The global bifurcation diagrams and exact multiplicity of equation (1) have been studied in many recent work. In particular, a systematic approach for the positive radially symmetric solutions of (1) when Ω is a ball was presented in Ouyang and Shi [OS1], [OS2] based on previous results by Korman, Li and Ouyang [...

Multi-parameter singular integrals