Existence and Asymptotic Behavior for the Ground State of Quasilinear Elliptic Equations

Abstract

In this paper, we are concerned with the existence and asymptotic behavior of minimizers of a minimization problem related to some quasilinear elliptic equations. Firstly, we prove that there exist minimizers when the exponent q is the critical one q*=2+4N{q^{*}=2+\frac{4}{N}}. Then, we prove that all minimizers are compact as q tends to the critical case q*{q^{*}} when aaq*{a>a_{q^{*}}}.

Keywords

• quasilinear elliptic equations
• minimization problem
• asymptotic behavior
• 35j20
• 35j60