A priori bounds for the positive solutions of super-linear indefinite weighted elliptic problems

In this work are given sufficient conditions on the nonlinearity and on certain potentials of a very general class of superlinear indefinite weighted elliptic problems of mixed type, to get uniform a priori bounds for their positive solutions. To perform our results, we adapt to our more general setting some of the rescaling arguments and Liouville type theorems used previously by H. Amann and J. Lopez-Gomez in Sec.4 of [1]. Monotonicity methods, rescaling arguments and Liouville type theorems are among the main technical tools used to carry out our analysis.