LIOUVILLE TYPE RESULTS FOR SYSTEMS OF ELLIPTIC INEQUALITIES WITH GRADIENT TERMS

Roberta Filippucci (Università degli Studi di Perugia, Italia)

We discuss some recent results about  non coercive elliptic multipower systems of divergence type, which include  $p$-Laplacian type operators  as well as mean curvature operators, and whose right hand sides depend on the product of both components of the solution and on a gradient factor. We are interested in Liouville type results, namely when any nonnegative nontrivial entire weak solution (non necessarily radial) is constant. For nontrivial solutions we intend that both components are nontrivial. The key ingredient of the proof technique is the method of test functions. No use of comparison and maximum principles or assumptions on symmetry  or behavior at infinity of the solutions is required.