Multiple positive solutions for elliptic equations involving a concave term and critical Sobolev–Hardy exponent

Multiple positive solutions for a quasilinear elliptic problem involving critical Sobolev–Hardy exponents and concave–convex nonlinearities

“…Remark 1.3. As p = 2 and 0 ≤ µ <μ 2 =  N−2 2  2 , Theorem 1.1 is the same as the known results (for p = 2 and s = 0, see [17]) and an improvement of the main results of [7,14]. The results of Theorem 1.1 are new in the case of p = 2, 0 ≤ µ <μ 2 , 0 < s < 2 and 0 ≤ t < 2.…”

“…Some authors also studied the singular problems with Sobolev-Hardy critical exponents (the case when t ̸ = 0); see [14][15][16][17][18][19] and the references therein.…”

Existence of positive solutions for a fractional elliptic problems with the Hardy-Sobolev-Maz’ya potential and critical nonlinearities

“…For the case s = 1 and λ = 1, Ding and Tang in [17] obtained the existence of positive solutions for problem (1) by the variational methods and some analysis techniques with f satisfying the (AR) condition. For related papers on the semilinear elliptic equations with Hardy-Sobolev critical exponents of (1) for s = 1, we just mention [18,19] and the references therein.…”

Multiple positive solutions for semilinear elliptic equations involving multi-singular inverse square potentials and concave–convex nonlinearities

“…x ∈ ∂Ω, (1.2) have been extensively studied, and the existence and multiplicity results for positive solutions have been obtained; see [4][5][6][7][8] and references therein.…”