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Báo cáo hóa học: " On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian | Guiro et al. Advances in Difference Equations 2011 2011 32 http www.advancesindifferenceequations.eom content 2011 1 32 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access On the solvability of discrete nonlinear Neumann problems involving the p x -Laplacian Aboudramane Guiro 1 Ismael Nyanquini1 and Stanislas Ouaro2 Correspondence ouaro@yahoo.fr 2Laboratoire d Analyse Mathématique des Equations LAME UFR. Sciences Exactes et Appliquées Université de Ouagadougou 03 BP 7021 Ouaga 03 Ouagadougou Burkina Faso Full list of author information is available at the end of the article Springer Abstract In this article we prove the existence and uniqueness of solutions for a family of discrete boundary value problems for data f which belongs to a discrete Hilbert space W. 2010 Mathematics Subject Classification 47A75 35B38 35P30 34L05 34L30. Keywords Discrete boundary value problem critical point weak solution electro-rheological fluids 1 Introduction In this article we study the following nonlinear Neumann discrete boundary value problem í- A d k - 1 Au k - 1 u k i k u k f k k e Z 1 T 1 1 1 Au 0 Au T 0 where T 2 is a positive integer and Am A m A 1 - u k is the forward difference operator. Throughout this article we denote by Z a b the discrete interval a a 1 . b where a and b are integers and a b. We also consider the function space w v Z 0 T 1 R such that Av 0 Av T 0 1 2 where W is a T-dimensional Hilbert space 1 2 with the inner product T 1 T u v y Au k 1 Av k 1 y u k v k Vu v e w. 1 3 k 1 k 1 The associated norm is defined by . T 1 T 2 huh l Au k - 1 2 u k 2 . 1 4 k 1 k 1 For the data f and a we assume the following f Z 1 T R 1 5 2011 Guiro et al licensee Springer. This is an Open Access article distributed under the terms ofthe Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Guiro et al. Advances