Asymptotic behavior and existence of solutions for singular elliptic equations

Abstract

We study the asymptotic behavior, as γ tends to infinity, of solutions for the homogeneous Dirichlet problem associated to singular semilinear elliptic equations whose model iswhere Ω is an open, bounded subset of R N and f is a bounded function. We deal with the existence of a limit equation under two different assumptions on f : either strictly positive on every compactly contained subset of Ω or only nonnegative. Through this study we deduce optimal existence results of positive solutions for the homogeneous Dirichlet problem associated to −∆v + |∇v| 2 v = f in Ω.

Comparison principle for elliptic equations with mixed singular nonlinearities

“…which, for = 0, was extensively studied in the past, see for instance [1,2,3,20,25]. The previous discussion could be formalized and the existence and uniqueness results given in the current paper could provide information regarding problem (1.4).…”

Existence and regularity of solutions to elliptic equation with singular convection term and lower order term

“…We are going to verify the following estimates in a similar way to previous studies. 23,25 Lemma 3.2. Suppose that u n is the solution to problem (3.1) given by Lemma 3.1, and for every…”

1-Laplacian type problems with strongly singular nonlinearities and gradient terms

“…If p = 2 and g(s) ∼ s −θ one may refer to [12,8,9,32,33] and references therein, while the case p > 1 has also been considered ( [54,53,20]). Observe that, in any cases, the threshold θ = 1 is shown to be critical in order to get global finite energy solutions for a general nonnegative datum f (see also the discussion in [27]).…”