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Some remarks on critical point theory for nondifferentiable functionals. (English) Zbl 0923.35049
The authors study the existence of critical points of nondifferentiable functionals $$J$$ of the kind $J(v)= \int_\Omega A(x,v)|\nabla v|^2- F(x,v)$ with $$A(x,v)$$ 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 hypotheses. Since $$J$$ is just differentiable along bounded directions, a suitable compactness condition is introduced.

##### MSC:
 35J20 Variational methods for second-order elliptic equations 49J52 Nonsmooth analysis
##### Keywords:
existence; compactness condition
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