Existence and multiplicity of positive solutions for a singular system via sub-supersolution method and Mountain Pass Theorem

Some recent results on singular p-laplacian systems

“…where K i ∈ L ∞ (Ω), α i < 0, and h ∈ C 1 (Ω × R 2 ) satisfy appropriate conditions that permit the use of variational methods. Theorem 1.7 of [5] gives two positive solutions provided max i=1,2 K i ∞ is sufficiently small. Finally, [50] addresses singular p(x)-Laplacian systems with nonlinear boundary conditions.…”

“…As far as we know, till today, much less attention has been paid to multiplicity of solutions. Actually, we can only mention the papers [67,12,26,5,50]. The first deals with singular p(x)-Laplacian systems while the second is devoted to quasi-linear problems driven by (Φ 1 , Φ 2 )-Laplace operators.…”

Some recent results on singular $ p $-Laplacian systems

“…As far as we know, till today, much less attention has been paid to multiplicity of solutions. Actually, we can only mention the papers [68,12,26,5,49]. The first deals with singular p(x)-Laplacian systems while the second is devoted to quasilinear problems driven by (Φ 1 , Φ 2 )-Laplace operators.…”

“…Two smooth solutions are obtained combining sub-super-solution methods with the Leray-Schauder topological degree. A different approach is adopted in [5]. The differential operators, which include the r-Laplacian as a special case, are neither homogeneous nor linear, while…”

A singular Schrödinger-Maxwell system

“…Some related results can be found in [10,21,23,24], in general for weak singularities (γ ∈ (0, 1) with the exception of [24]), and based on a variational framework. Other results for other type of system with singular nonlinearities can be found for instance in [1,13,22]. Motivated by the above context, the main aim of this work is to study the singular Schrödinger-Maxwell system (1.1), including the non variational case and the strongly singular one.…”