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We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems
where , , is a bifurcation parameter, is an evolution parameter, and is either or . We prove that the corresponding bifurcation curve is -shape. Thus, the exact multiplicity of positive solutions can be obtained.
We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than Cε^{2}|log(h)|^{-1}, where h and ε denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already known...
This work is concerned with the equilibrium configurations of elastic structures
in contact with Coulomb friction. We obtain a variational formulation of this
equilibrium problem. Then we propose sufficient conditions for the existence of
an infinity of equilibrium configurations with arbitrary small friction
coefficients. We illustrate the result in two space dimensions with a
simple example.
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