Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms
Texas State University-San Marcos, Department of Mathematics
We show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem -Δu = k(x)g(u) + λ|∇u|q, u > 0, x ∈ Ω, u|∂Ω = 0, where Ω is a bounded domain with smooth boundary in ℝN. We use the Karamata regular varying theory, a perturbed argument, and constructing comparison functions.
Semilinear elliptic equations, Dirichlet problem, Singularity, Nonlinear convection terms, Karamata regular variation theory, Unique solution, Exact asymptotic behaviour
Zhang, Z. (2006). Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms. <i>Electronic Journal of Differential Equations, 2006</i>(93), pp. 1-8.