A Maximum Principle for an Elliptic System and Applications to Semilinear Problems

Djairo G. de Figueiredot () and Enzo Mitidieri
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Djairo G. de Figueiredot: Universidade de Brasilia, Departamento de Matematica
Enzo Mitidieri: Universith Degli Studi di Trieste, Istituto di Matematica

A chapter in Djairo G. de Figueiredo - Selected Papers, 1986, pp 225-238 from Springer

Abstract: Abstract The Dirichlet problem in a bounded region for elliptic systems of the form (*) $$ - \Updelta u = f\left( {x,u} \right) - v,\quad - \Updelta v = \delta u - \gamma v $$ is studied. For the question of existence of positive solutions the key ingredient is a maximum principle for a linear elliptic system associated with (*). A priori bounds for the solutions of (*) are proved under various types of growth conditions on f. Variational methods are used to establish the existence of pairs of solutions for (*).

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02856-9_17

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DOI: 10.1007/978-3-319-02856-9_17

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