Affiliation:
1. Department of Mathematics , School of Science , Wuhan University of Technology , Wuhan 430070 , P. R. China
Abstract
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
+
4
N
{q^{*}=2+\frac{4}{N}}
. Then, we prove that all minimizers are compact as q tends to the critical case
q
*
{q^{*}}
when
a
<
a
q
*
{a<a_{q^{*}}}
is fixed. Moreover, we find that all the minimizers must blow up as the exponent q tends to the critical case
q
*
{q^{*}}
for any fixed
a
>
a
q
*
{a>a_{q^{*}}}
.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Statistical and Nonlinear Physics
Cited by
6 articles.
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