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POSITIVITY AND NEGATIVITY OF SOLUTIONS TO n × n WEIGHTED SYSTEMS INVOLVING THE LAPLACE OPERATOR ON R N
2012
Electronic Journal of Differential Equations
unpublished
We consider the sign of the solutions of a n × n system defined on the whole space R N , N ≥ 3 and a weight function ρ with a positive part decreasing fast enough, −∆U = λρ(x)M U + F, where F is a vector of functions, M is a n×n matrix with constant coefficients, not necessarily cooperative, and the weight function ρ is allowed to change sign. We prove that the solutions of the n × n system exist and then we prove the local fundamental positivity and local fundamental negativity of the
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