We Consider the nonlinear Dirichlet problem: <IMG SRC="/fbpe/img/proy/v21n3/img04-01.gif" WIDTH=350 HEIGHT=56> where . omega <FONT FACE=Symbol>Î</FONT> R N is a bounded open domain, F : omega chi R -> R is a carath´eodory function and DuF(x; u) is the partial derivative of F. We are interested in the resolution of problem (1) when F is concave. Our tool is absolutely variational. Therefore, we state and prove a critical point theorem which generalizes many other results in the literature and leads to the resolution of problem (1). Our theorem allows us to express our assumptions on the nonlinearity in terms of F and not of <FONT FACE=Symbol>Ñ</FONT>F. Also, we note that our theorem doesn t necessitate the verification of the famous compactness condition introduced by Palais-Smale or any of its variants