On the quasilinear elliptic problems with critical Sobolev–Hardy exponents and Hardy terms

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.…”

Multiplicity of solutions for a class of quasilinear elliptic equation involving the critical Sobolev and Hardy exponents

“…Furthermore, we consider more general nonlinearity than is considered in [14,15]. Hence, we make a improvement of the main results of [2,14,15,20]. …”

“…(1.1) are obtained in [14]. Chen and Li [15] obtained that the existence of infinitely many solutions by using minimax procedure in the case µ = 0 and f (x, u) = k(x)|u| r−2 u (1 < r < Np N −p ).…”

Multiple Symmetric Results for Quasilinear Elliptic Systems Involving Singular Potentials and Critical Sobolev Exponents inRN

“…The mathematical interest lies in the fact that these problems like (2) are doubly critical due to the presence of the Sobolev embedding and the singularities. For this reason, many existence, nonexistence, and multiplicity results of nontrivial solutions for the single equations like (2) have been established with different assumptions on the potentials ( ), ℎ( ) and the parameters , , and ; we refer to [2][3][4][5][6][7][8] and the references therein. In a recent paper, Deng and Jin [9] considered the following single semilinear elliptic problem:…”