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Báo cáo toán học: " Existence and multiplicity of solutions for nonlocal p(x)-Laplacian equations with nonlinear Neumann boundary conditions"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Existence and multiplicity of solutions for nonlocal p(x)-Laplacian equations with nonlinear Neumann boundary conditions | Boundary Value Problems SpringerOpen0 This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text HTML versions will be made available soon. Existence and multiplicity of solutions for nonlocal p x -Laplacian equations with nonlinear Neumann boundary conditions Boundary Value Problems 2012 2012 1 doi 10.1186 1687-2770-2012-1 Erlin Guo guoerlin@lzu.edu.cn Peihao Zhao zhaoph@lzu.edu.cn ISSN 1687-2770 Article type Research Submission date 29 August 2011 Acceptance date 4 January 2012 Publication date 4 January 2012 Article URL http www.boundaryvalueproblems.com content 2012 1 1 This peer-reviewed article was published immediately upon acceptance. It can be downloaded printed and distributed freely for any purposes see copyright notice below . For information about publishing your research in Boundary Value Problems go to http www.boundaryvalueproblems.com authors instructions For information about other SpringerOpen publications go to http www.springeropen.com 2012 Guo and Zhao licensee Springer. This is an open access article distributed under the terms of the 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. Existence and multiplicity of solutions for nonlocal p x -Laplacian equations with nonlinear Neumann boundary conditions Erlin Guo and Peihao Zhao School of Mathematics and Statistics Lanzhou University Lanzhou 730000 P. R. China Corresponding author guoerlin@lzu.edu.cn Email address zhaoph@lzu.edu.cn Abstract In this article we study the nonlocal p x -Laplacian problem of the following form a j- px Vu p x u p x dxj -drv Vu P x -2Vu u p x -2u I G f- F x u dx f x u in - a J- p 1xy Vu p x u p x dx Vu p 2 @ g x u on Ỡ- where - is a smooth bounded domain and V is the outward normal vector on the boundary d- and F x u G f x t dt. By using the variational method and .