A Maximum Principle for an Elliptic System and Applications to Semilinear Problems.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This document studied a Dirichlet problem in a bounded region for elliptic systems. 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 .
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