p. 209 - 214 On the uniqueness result for the Dirichlet problem and invexity M. Płócienniczak 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; PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |