Infinitely many solutions for quasilinear equations with critical exponent and Hardy potential in R^N

Gao, Fengshuang; Guo, Yuxia

In this paper, we consider the following critical quasilinear equation with Hardy potential:{−∑Ni,j = 1 Dj(aij(u)Diu) 1/2∑Ni,j = 1a′ij(u)DiuDju a(x)u = ν|u|q−2u μu/|x|2 |u|2∗−2u,in RN, u(x) → 0 as |x| → ∞, where aij(u)∈C1(R,R), ν > 0, 0 ≤ μ 0, μ = (N−2)2/4, 2∗ = 2N/N−2 is the Sobolev critical exponent. And a(x)a(x) is a finite, positive potential function satisfying suitable decay assumptions. By using truncation method combining with the regularization approximation approach and compactness arguments, we prove the existence of infinitely many solutions for this equation.

CRITICAL exponents; EQUATIONS; POTENTIAL functions; MATHEMATICAL regularization

Discrete & Continuous Dynamical Systems: Series A, 2020, Vol 40, Issue 9, p5591

1078-0947

Academic Journal

10.3934/dcds.2020239