We consider solutions to the nonlinear eigenvalue problem (*) [FORMULA PRESENT], where (*) is a quasilinear strongly coupled second order elliptic system of partial differential equations and Ω ⊆ Rn is a smooth bounded domain. We obtain lower bounds for λ in the case where f(x, u) has linear growth, and relations between λ,Ω and ess sup |u| when f(x, u) has sub- or superlinear growth. The estimates are based on integration by parts and application of certain Sobolev inequalities. We briefly discuss extensions to' higher order systems.
ASJC Scopus subject areas
- Applied Mathematics