On Semilinear Elliptic Equation with Measurable Nonlinearity

We consider a semilinear elliptic equation in a bounded domain with zero boundary conditions. The nonlinearity is discontinuous and monotone, but it is not a Carath\'eodory's function. The existence theorem has been proved.Comment: this paper has been withdrawn by the author due to the results on the whole are not ne

A Note on the Caristi Fixed Point Theorem

We generalise the Caristi Fixed Point Theorem to the mappings of the complete semi-metric spaces.Comment: this paper has been withdrawn by the author due to the results on the whole are standar

On some abstract version of the Cauchy-Kowalewski Problem

We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.Comment: 6 pages, AMS-LaTe

Lagrangian Systems with non-smooth constraints

The Lagrange-d'Alembert equations with constraints belonging to $H^{1,\infty}$ have been considered. A concept of weak solutions to these equations has been built. Global existence theorem for Cauchy problem has been obtained