Some remarks on critical point theory for nondifferentiable functionals |
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Authors: | David Arcoya Lucio Boccardo |
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Institution: | (1) Departamento de Análisis Matemático, Universidad de Granada, E-18071 Granada, Spain, ES;(2) Dipartimento di Matematica, Università di Roma 1, I-00100 Roma, Italy, IT |
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Abstract: | In this paper we study the existence of critical points of nondifferentiable functionals J of the kind with A (x,z) a Carathéodory function bounded between positive constant and with bounded derivative respect to the variable z, and F (x,z) is the primitive of a (Carathéodory) nonlinearity f (x,z) satisfying suitable hipotheses. Since J is just differentible along bounded directions, a suitable compactness condition is introduced. Its connection with coercivity
is discussed. In addition, the case of concave-convex nonlinearities f (x,z), unbounded coefficients A (x,z) and related problems are also studied.
Received December 19, 1997 |
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