Abstract
We investigate the existence and nonexistence of positive solutions for the quasilinear elliptic inequality LAu=−div[A(x,u,∇u)]≥(Iα⁎up)uq in Ω, where Ω⊂RN,N≥1, is an open set. Here Iα stands for the Riesz potential of order α∈(0,N), p>0 and q∈R. For a large class of operators LA (which includes the m-Laplace and the m-mean curvature operator) we obtain optimal ranges of exponents p,q and α for which positive solutions exist. Our methods are then extended to quasilinear elliptic systems of inequalities.
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