We prove the existence of solutions ( λ , v ) ∈ R × H 1 Ω elliptic problem { − Δ + V x = p in Ω, > 0 ∫ 2 d ρ . Any solving such (for some is called a normalized solution, where normalization settled L Here either whole space N or bounded smooth domain which case we assume ≡ and homogeneous Dirichlet Neumann boundary conditions. Moreover, < if ≥ 3 Normalized appear different contexts, as study N...

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers several Schwarz alternating methods for nonlinear elliptic p...

In this paper we study several overlapping domain decompo sition based iterative algorithms for the numerical solution of some non linear strongly elliptic equations discretized by the nite element methods In particular we consider additive Schwarz algorithms used together with the classical inexact Newton methods We show that the algorithms con verge and the convergence rates are independent o...