Shramenko V. The index of a critical point for nondifferentiable elliptic operators

The dissertation is devoted to the computation of the index of a critical point for nondifferentiable nonlinear elliptic operators of the second and higher orders. These results follow from the theorem on the index of a critical point for abstract nondifferentiable operators of type (S+), which was proved by the author. Also the applications of the index formula to relevant bifurcation problem were given. Topological characteristics for nonlinear elliptic operators with strong coefficients growth in the main and low order parts are also studied in this work. Essential attention was paid to regularity results for quasilinear elliptic equations of the second and higher orders, with a small parameter.