Iterative solution for a singular nonlinear elliptic problem

Positive solutions for singular nonlinear elliptic equations

“…The result of theorem 3.19 was proved in [16] for the particular case L = −∆, −1 < q < 0 < p < 1, using regularization and sub-and supersolutions. Theorem 3.19 also extends [41, theorem 1.1], [12, theorem 1] and [49, theorem 3.1] (see also [45]).…”

“…The result in theorem 3.13 seems to be new for N 2 and −1 < q < 0 and extends [41, theorem 1.2], [51, theorem 1], [49, theorem 3.3] (see also [45]), [22] and [20, lemma 4.11], where the case −1 < p < 0 < q < 1 is treated. The result in theorem 3.13 seems to be new for N 2 and −1 < q < 0 and extends [41, theorem 1.2], [51, theorem 1], [49, theorem 3.3] (see also [45]), [22] and [20, lemma 4.11], where the case −1 < p < 0 < q < 1 is treated.…”

“…This means, invoking the strong maximum principle, that, for such small λ > 0, any solution of (3.5) must be such that u < cϕ 1 for all c > 0, which proves the non-existence of positive solutions and completes the proof of the theorem. [49, theorem 3.3] (see also [45]), [22] and [20, lemma 4.11], where the case −1 < p < 0 < q < 1 is treated. Zhang [51] also shows that there is no solution in C 2 (Ω) ∩ C 1 (Ω) if q −1 (see also [11]).…”

The existence and non-existence of positive solutions to a singular quasilinear elliptic problem in

“…Boundary value problem for singular elliptic equations have been intensively studied in recent years and we refer the reader to Gui and Lin [1], Lazer and McKenna [2], Zhang and Cheng [3], Sun and Wu [4], Yao and Zhao [5], Sun et al [6], Coclite and Palmieri [7], Zhang [8], Cirstea et al [9], Perera and Silva [10], Huang [11] and references therein.…”