Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities

By N. Hirano, C. Saccon, Naoki Shioji. Advances in Differential Equations, 2004

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Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation (2007, methodology): “The critical case q = 2∗ − 1 and N ≥ 3 was settled almost simultaneously in Haitao [29] and Hirano, Saccon, and Shioji [31] by two different methods: Perron’s method and Nehari’s method, respectively.”
Multiplicity of positive solutions for a singular and critical problem (2009, methodology): “The critical case q = 2 − 1 and N ≥ 3 was settled almost simultaneously in [6] and [7] by two different methods: Perron’s method and Nehari’s method, respectively.”
A multiplicity results for a singular problem involving the fractional p-Laplacian operator (2016, background): “[24], Giacomoni and Saoudi [25], Adimurthi and Giacomoni [26] and references therein.”
Brezis–Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem (2008, background): “1) were recently studied by Sun, Wu and Long [24], Haitao [14] and the authors [16].”