Non-existence of dead cores in fully nonlinear elliptic models

We investigate non-existence of non-negative dead core solutions for the problem [Formula: see text] Here, is a bounded smooth domain, fully nonlinear elliptic operator, sign-changing weight, text], and text]. show that this has no nontrivial if either close enough to or negative part sufficiently small. In addition, we obtain existence uniqueness positive solution under these conditions on Our results extend previous ones established in semilinear case, are new even simple model where uniformly matrix.