Main scientific achievements 
 Negative spectra of quasielliptic equations were studied, their number was estimated;
 the results expressing quality properties of divergent and nondivergent structure second order degenerate and nondegenerate elliptic and parabolic equations were obtained;
 equivalence of Wiener and Petrovsky type criteria of regularity of the point of a boundary value problem for parabolic equations was proved;
 quality properties of solutions of nondivergent structure, discontinuous coefficient parabolic equations were studied;
 ”conditional” wellposedness of inverse problems with coefficient for linear, nonlinear, quasilinear parabolic equations and system of equations was studied;
 quality properties of the solutions of a class of pseudohyperbolic and pseudoparabolic equations were investigated;
 parabolic potentials were estimated in singular domains;
 asymptotics of the solutions of nonlinear equations near the singular point was studied;
 Poincare inequality for second order quasilinear elliptic equations was proved;
 the questions of existence and uniqueness of solutions of the Dirichlet and Neumann problem for discontinuous coefficient Cordes type linear and quasilinear elliptic equations were studied;
 theorems on a removable singularity of Carleson type for degenerate equations were proved;
 theorems on a removable singularity and theorems on the qualitative properties for pLaplacian type quasilinear equations with degenerating principal part were proved;
 PoincareSobolev and Hardy type uniform and nonuniform inequalities were proved;
 weighted Hardy inequalities in the Lebesgue spaces with a variable exponent were proved;
 existence of global solutions of semilinear elliptic and parabolic type equations were studied, exact estimations for the existence of solutions were found;
 asymptotics of solutions satisfying the Neumann condition near the infinity was studied;
 uniqueness of solution of linear ordinary differential and partial equations without boundary condition was studied;
 behavior of Zaremba problem for second order degenerate elliptic equations in the boundary was studied, regularity of congruence point in special spherical layers was investigated.
