On a Dirichlet problem in bounded domains with singular nonlinearity

On the definition of the solution to a semilinear elliptic problem with a strong singularity at u=0

“…The problem was then studied by many authors, among which we will quote the works of C.A. Stuart [25] [9], D. Arcoya and L. Moreno-Mérida [2], and F. Oliva and F. Petitta [23].…”

A Singular Semilinear Elliptic Equation with a Variable Exponent

“…Some existence and regularity results have been obtained in [3,[6][7][8] but, to our knowledge, the role played by the behavior of γ(x) near the boundary has not been studied. We are inspired by [2] and we work with approximations, by considering an increasing sequence u n of solutions to nonsingular problems.…”

“…Regarding existence and regularity results for the case where g(x, s) = f(x) u γ , for f ∈ L m (Ω), we refer to the papers [1][2][3]14]. For existence and homogenization results for this kind of problems, we refer to the papers [6][7][8].…”

Asymptotic behavior and existence of solutions for singular elliptic equations

“…u γ+1 2 ∈ W 1,2 0 (Ω). Existence and regularity of solutions of (1.1) with data in suitable Lebesgue space or with measure data are also studied in [18,11,12,35,26,17], while, in case of a nonlinear principal part, we refer to [10,22,33]. We underline also the study of qualitative properties of solutions of (1.1) contained in [13,24].…”