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Global continuation for quasilinear elliptic systems on \(\mathbb{R}^N\) and the equations of elastostatics. (English) Zbl 1198.35044

Summary: We consider quasilinear systems of second order elliptic equations on \(\mathbb R^N\). 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 infinity. 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.

MSC:

35B60 Continuation and prolongation of solutions to PDEs
47H11 Degree theory for nonlinear operators
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
35J47 Second-order elliptic systems
74B20 Nonlinear elasticity
35J62 Quasilinear elliptic equations
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