On certain nonlinear elliptic systems with indefinite terms.
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Publisher
Electronic Journal of Differential Equations (EJDE)[electronic only]
Abstract
The purpose of this article is to nd positive solutions to the system
pu = m(x)@H
@ u(u; v) in
qv = m(x)@H
@ v(u; v) in
(1:1)
u = v = 0 on@
where
is a bounded regular domain of RN; with a smooth boundary @
;
pu := div (j ru jp2 ru) is the p Laplacian with 1 < p < N;m is a continuous
function on
which changes sign , and H is a potential function which will be speci ed later .
The case where the sign of m does not change has been studied by F . de
Th e lin and J . V e lin [ 9 ] . These authors treat the system ( 1 . 1 ) with a function H
having the following properties
HThere(x; uexists
; v) CC(j>0
ujp0
;
+
for j v jall0q ) x 2
; for all (u; v) 2 D3 such
that 0
There exists C0 > 0; for all x 2
; for all (u; v) 2 D2 such that H(x; u; v)
C0
There exists a positive function a in L1(
); such that for each x 2
and
(u; v) 2 D1 \ R2
+;H(x; u; v) = a(x)u +1v +1;