Multiple solutions for quasilinear equation involving Hardy critical Sobolev exponents - Gao, Fengshuang; Guo, Yuxia (Topological Methods in Nonlinear Analysis, 2020)
We consider the following quasilinear elliptic equation with critical Sobolev and Hardy-Sobolev exponents: \[ cases -_i,j=1^ND_j(b_ij(v)D_iv)+12_i,j=1^N b_ij’(v)D_ivD_jv =|v|^2^*_sq-2v|x|^s+μ|v|^2^*q-2v+a(x)|v|^2q-2v &in Ω, v=0 &on Ω, cases \] where b_ijC^1(R,R) satisfies the growth condition |b_ij(t)||t|^2(q-1) at infinity, q≥1, μ≥0, 0< s< 2, 2^*_s=2(N-s)/(N-2), 2^*=2N/(N-2), 0Ω and Ω is a bounded domain in R^N. In this paper, we will investigate the effects of the lower order terms a(x)|v|^2q-2v and the growth of b_ij(v) at infinity on the existence of infinitely many solutions for the above equations.