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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

BOUKHRISSE, HAFIDA  and  MOUSSAOUI, MIMOUN. CRITICAL POINT THEOREMS AND APPLICATIONS. Proyecciones (Antofagasta) [online]. 2002, vol.21, n.3, pp.261-276. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172002000300004.

We Consider the nonlinear Dirichlet problem: where . W Î R N is a bounded open domain, F : W C 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 ÑF. 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

Keywords : Critical point theory; convexity conditions; Elliptic semilinear problem.

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