Perturbation methods in semilinear elliptic problems involving critical hardy-sobolev exponent

Positive Solutions for Elliptic Problems with the Nonlinearity Containing Singularity and Hardy-Sobolev Exponents

“…In recent years, people have paid much attention to the existence of solutions for problems with the Sobolev critical exponent (the case that s = 0) (see [16][17][18][19][20][21] and the references therein); some authors also considered the singular problems with the Hardy-Sobolev critical exponent (the case that s ≠ 0) (see [22][23][24][25][26][27] and the references therein).…”

Positive Radial Solutions for a Class of Semilinear Elliptic Problems Involving Critical Hardy-Sobolev Exponent and Hardy Terms

“…In addition to the lack of compactness, there are more intrinsic obstructions involving the nature of its critical points. Based on a suitable use of an abstract perturbation method in critical point theory discussed in [5] [13] [14], we show that the semilinear elliptic problem with Hardy-Sobolev exponent and Hardy singular terms has at least a positive radial solution.…”