An extension of maximum principle with some applications

Abstract

Let U ⊆ R n (res. D ⊂ R n ) be an open (res. a compact) subset, and let L be an elliptic operator defined on C 2 (U, R) (res. C 2 (D, R) ). In the present paper, we are going to extend the maximum principle for the function f ∈ C 2 (U, R) (res. f ∈ C 2 (D, R) ) satisfying the equation Lf = ε, where ε is a real everywhere nonzero continuous function on U (res. D). Finally, we obtain some applications in mathematics and physics.