Elliptic Equations with Decreasing Nonlinearity I : Barrier method for Decreasing Solutions

In this note, we establish existence theorems for positive and classical solutions of the problem (Ea.tad ) below using a barrier method. Moreover we show that the existence of such solutions can be obtained from the sole existence of a supersolution or of a subsolution of the equation. AMS Subject Classification. 35J70, 35J65 34C10