Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential

Abstract

Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations −Δpu − μ |x| p |u| p−2 u + m|u| p−2 u = f (u), x∈ R N , where 1 < p < N, 0 ≤ μ < ((N − p)/p) p , m > 0 and f is a continuous function.

Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations

“…We can prove Theorem 1.3 in the case µ ≤ 0 similarly. In the case when 0 < µ <μ, the same estimates were obtained by the authors in [20] for positive radial weak solutions to the following equation…”

“…Theorem 1.3 can be proved by the same argument as that of [20 Recall that Γ µ is defined as in (1.8). To prove Theorem 1.3, it is enough to prove that + o(r δ ) as r → 0, for some δ ∈ (0, 1).…”

Uniqueness of Single Peak Solutions for a Kirchhoff Equation

“…Proof. Using the comparison principle of He and Xiang [13], we can obtain (11), which also can be found in [5].…”