On singular quasi-monotone (p, q)-Laplacian systems

Abstract

We combine the sub-and supersolution method and perturbation arguments to obtain positive solutions of singular quasi-monotone (p, q)-Laplacian systems.

Positive solutions for infinite semipositone/positone quasilinear elliptic systems with singular and superlinear terms

“…The sublinear condition α 2 < q − 1 and β 1 < p − 1 for singular systems of type (1.1) have been thoroughly investigated. For a complete overview on the study of the infinite positone problem (1.1) we refer to [1,2,15,17], while for the study of the infinite semipositone problem (1.1), we cite [5,13,14]. We also mention [6,7] focusing on the semilinear case of (1.1), that is, when p = q = 2.…”

Quasilinear and singular systems: The cooperative case

“…However concerning the case of one single equation, we can quote the results in Aranda-Godoy [3], Giacomoni-Schindler-Takac [15] and Perera-Silva [22]. In El Manouni-Perera-Shivaji [21] the authors study by an approximation procedure a class of quasilinear cooperative systems under less general assumptions than ours in the present paper. Furthermore, the results in [21] do not deal with strongly singular nonlinearities and no uniqueness result is obtained.…”

“…In El Manouni-Perera-Shivaji [21] the authors study by an approximation procedure a class of quasilinear cooperative systems under less general assumptions than ours in the present paper. Furthermore, the results in [21] do not deal with strongly singular nonlinearities and no uniqueness result is obtained. Concerning the uniqueness of solutions, the point is that equations involving quasilinear elliptic operators yield additional difficulties for obtaining the validity of the strong comparison principle (see Cuesta-Takac [7], Fleckinger-Takac [11], Giacomoni-Schindler-Takac [15] and Vazquez [25]) which requires the C 1 -regularity for solutions.…”

Singular Quasilinear Elliptic Systems With Gradient Dependence

“…The particular case in singular system (P) when the convection terms ∇u and ∇v are removed has received a special attention. Relevant contributions regarding this topic can be found in [1,9,10,11,16,20,21,22] and the references given there.…”