Electron. J. Diff. Eqns.,
Vol. 2003(2003), No. 99, pp. 118.
Qualitative properties of solutions for quasilinear elliptic equations
Zhenyi Zhao
Abstract:
For several classes of functions including the
special case
,
,
we obtain Liouville
type, boundedness and symmetry results for solutions of the
nonlinear
Laplacian problem
defined on the whole space
.
Suppose
is a solution. We have that either
(1) if
does not change sign, then
is a constant
(hence,
or
or
); or
(2) if
changes sign, then
,
moreover
on
; or
(3) if
on
and the level set
lies
on one side of a hyperplane and touches that hyperplane, i.e.,
there exists
and
such that
for all
,
then
depends on one variable only (in the direction of
).
Submitted May 29, 2003. Published September 25, 2003.
Math Subject Classifications: 35J15, 35J25, 35J60.
Key Words: Quasilinear elliptic equations, comparison Principle,
boundary blowup solutions, moving plane method, sliding method,
symmetry of solution.
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Zhenyi Zhao
Department of Mathematical Sciences
Tsinghua University
Beijing, 100084, China
email: zhaozhenyi@tsinghua.org.cn

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