TITLE:
General Boundary Value Problems for Nonlinear Uniformly Elliptic Equations in Multiply Connected Infinite Domains
AUTHORS:
Guochun Wen, Yanhui Zhang, Dechang Chen
KEYWORDS:
Boundary Value Problems; Nonlinear Elliptic Equations; Multiply Connected Infinite Domains
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.2 No.3,
August
30,
2013
ABSTRACT: This article discusses the general boundary value
problem for the nonlinear uniformly elliptic equation of second order in D (0.1) and the boundary
condition,(0.2) in a multiply
connected infinite domain D with the boundary T. The above boundary value problem is called Problem G.
Problem G extends the work [8] in which the equation (0.1) includes a nonlinear
lower term and the boundary condition (0.2) is more general. If the complex
equation (0.1) and the boundary condition (0.2) meet certain assumptions, some
solvability results for Problem G can be obtained. By using reduction to
absurdity, we first discuss a priori estimates of solutions and solvability for
a modified problem. Then we present results on solvability of Problem G.