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On the uniqueness result for the Dirichlet problem and invexity
Received: March 14, 2007; Accepted: October 8, 2007
Abstract. We provide an existence and uniqueness theorem for the Dirichlet problem
div Hz(y,Ñx(y)) = ÑxF(y,x(y)).
The assumption that both H and F are invex with respect to the second variable is imposed and the direct variational method is applied. The application is also shown.
Keywords: Dirichlet problem; calculus of variations; invexity; existence; uniqueness
AMS Subject classification: Primary: 26B25, 35A15, 35G30, 49J45;
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