Generalized Solutions to Boundary-Value Problems for Quasilinear Elliptic Equations on Noncompact Riemannian Manifolds

In the present work we develop approximation approach to evaluation of solutions to boundary-value problems for quasilinear equations of the elliptic type on arbitrary noncompact Riemannian manifolds. Our technique essentially bases on an approach from the papers of E. A. Mazepa and S. A. Korol’kov connected with introduction of equivalency classes of functions and representations. On the other hand, it generalizes the method of building of generalized solution to the Dirichlet problem for linear elliptic Laplace–Beltrami and Schrödinger equations in bounded domains in ℝn, which is described in details in the works of M. V. Keldysh and E. M. Landis. © 2018, Allerton Press, Inc.