Global Continuation for Quasilinear Elliptic Systems on ℝ N and the Equations of Elastostatics
Hicham G. Gebran, Charles A. Stuart · Advanced Nonlinear Studies · 2009
Abstract We consider quasilinear systems of second order elliptic equations on ℝ N . Using a continuation theorem based on the topological degree for C 1 - Fredholm maps, we derive global properties of a maximal connected set of solutions which decay exponentially to zero at in¯nity. These results are used to treat a problem concerning the equilibrium of an elastic body occupying the whole space and subjected to a one parameter family of localized external forces.