On solvability of elliptic boundary value problems via global invertibility

Abstract

In this work we apply global invertibility result in order to examine the solvability of elliptic equations with both Neumann and Dirichlet boundary conditions.

Solvability of Iterative Classes of Nonlinear Elliptic Equations on an Exterior Domain

“…The combination (X, d) creates a complete metric space for d in (11). Then, (X, ρ) constitutes a metric space for the value of ρ in (12). The equation expressing the connection between the two measures on X is ρ(y, z) ≤ d(y, z) for all y, z ∈ X.…”

“…In [10], again for d = 2, Ali-Shivaji discussed the existence of multiple positive solutions for λ >> 1 when F(0) = 0 = F (0) for β ∈ {1, 2}. In addition, in [11][12][13][14][15][16][17][18][19][20], relevant references to the most recent works on (1) can be found. Next, we quote some recent works on elliptic equations.…”