Maximum and minimum first eigenvalues for a class of elliptic operators
Carlo Pucci · Proceedings of the American Mathematical Society · 1966
By the maximum principle all the X's are positive (see [l]). Bounds for the X's were established under various hypotheses by Duffin [2], Protter-Weinberg [3]. Here we want to determine if A has a maximum or a minimum and for what operator in £„ the maximum or minimum occurs. Let Ma, ma denote the maximizing and minimizing operator relative to the class £a, that is for each fixed function u and fixed x: