Solutions of a quasilinear elliptic problem involving a critical Sobolev exponent and multiple Hardy-type terms

On a p-Laplace equation with multiple critical nonlinearities

“…since u is a non-negative extremal for (5). Hence, if equality would hold in (9), then 0 < c u = sup t≥0 Φ(tu) = sup t≥0 f (t).…”

“…The choice of the energy level involves the best constants in the Hardy-Sobolev inequalities (see (5) and (6) of Section 2). We are then led to considering the possible extremals for them.…”

Multiple positive solutions for a class of quasi-linear elliptic equations involving concave-convex nonlinearities and Hardy terms

“…Such kind of problem with critical exponents and nonnegative weight functions has been extensively studied by many authors. We refer, e.g., in bounded domains and for p = 2 to [4][5][6] and for p >1 to [7][8][9][10][11], while in ℝ N and for p = 2 to [12,13], and for p >1 to [3,[14][15][16][17], and the references therein.…”

Existence and multiplicity of solutions to a singular elliptic system with critical Sobolev–Hardy exponents and concave–convex nonlinearities

“…We refer, e.g., in bounded domains and for p = 2 to [4,3,5,6], and for general p > 1 to [7][8][9][10][11] and the references therein. For example, Kang in [11] studied the following elliptic equation via the generalized Mountain-Pass Theorem [12]:…”