Singular Quasilinear Elliptic Systems with (super-) Homogeneous Condition

Abstract

In this paper we establish existence, nonexitence and regularity of positive solutions for a class of singular quasilinear elliptic systems subject to (sub-, super-) homogeneous condition. The approach is based on subsupersolution methods for systems of quasilinear singular equations combined with perturbation arguments involving singular terms.2010 Mathematics Subject Classification. 35J75; 35J48; 35J92.

Existence and a priori estimates of solutions for quasilinear singular elliptic systems with variable exponents

“…However, it is worth notting that the obtained sub-and supersolution are quite different from the functions considered in the quoted papers, especially those constructed in [2,3]. Practically and contrary to preconceived ideas, the construction process of the sub-and super-solutions in the present work is broadly similar to the one used in the case of constant exponent problems (see, e.g., [7,18,19]), despite the loss of the homogeneity property of the operator ∆ p i (x) , which constitutes in itself a major obstacle to face. The crucial aspect of the argument is the new Mean Value Theorem (cf.…”

Nodal solutions for singular semilinear elliptic systems

“…It represents a serious difficulty to overcome and, as far as we know, is never handled in the literature even for singular problems in the scalar case. For more inquiries on the study of constant sign solutions for singular systems we refer to [11,10,9,4,5,7] and the references therein.…”

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.…”