Abstract
We prove non-existence and existence of entire positive solutions for a Schrodinger quasilinear elliptic system. To prove the non-existence, we combine a carefully-chosen test function with some results that we proved concerning the positivity of a kind of principal eigenvalue of a eigenvalue problem in RN with indefinite weights. Contrary to the existence, the non-existence results for this class of problems have not been studied very much in recent years. For the existence we mainly used upper and lower solution methods combined with comparison principles. Mathematics subject classification (2010): 35B08, 35B09, 35B53, 35J10, 35J57, 35J92.
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