This paper deals with the nonexistence and multiplicity of nonnegative, nontrivial solutions to a
class of degenerate and singular elliptic systems of the form{(- div (h1 (x) ?? u) = ? Fu (x, u, v), in ??,; - div
(h2 (x) ?? v) = ? Fv (x, u, v), in ??,) where ?? is a bounded domain with smooth boundary ???? in RN, N ??
2, and hi : ?? ?? [0, ??), hi ?? Lloc
1 (??), hi (i = 1, 2) are allowed to have "essential" zeroes at some points in
??, (Fu, Fv) = ?? F, and ? is a positive parameter. Our proofs rely essentially on the critical point theory tools
combined with a variant of the Caffarelli-Kohn-Nirenberg inequality in [P. Caldiroli, R. Musina, On a
variational degenerate elliptic problem, NoDEA Nonlinear Differential Equations Appl. 7 (2000) 189-199].
?? 2009 Elsevier Inc. All rights reserved.
