Generalized solutions of boundary-value problems for quasilinear elliptic equation on noncompact Riemannian manifolds

The paper is devoted to the development of approximative approach to the construction of solutions to boundary-value problems for quasilinear elliptic equations on arbitrary noncompact Riemannian manifolds. Methods of studies essentially rely on an approach based on the introduction of equivalence classes of functions on Riemannian manifold (papers of E. Mazepa and S. Korol'kov). It also summarizes the methodology for constructing a generalized solution to the Dirichlet problem for linear elliptic equations in bounded domains of $\mathbb{R}^n$ (papers of M. Keldysh and E. Landis).