tailieunhanh - Báo cáo hóa học: "DIFFERENTIAL INEQUALITIES METHOD TO nTh-ORDER BOUNDARY VALUE PROBLEMS"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: DIFFERENTIAL INEQUALITIES METHOD TO nTh-ORDER BOUNDARY VALUE PROBLEMS | DIFFERENTIAL INEQUALITIES METHOD TO nTh-ORDER BOUNDARY VALUE PROBLEMS GUANGWA WANG MINGRU ZHOU AND LI SUN Received 31 March 2005 Revised 18 October 2005 Accepted 7 December 2005 By the theory of differential inequality bounding function method and the theory of topological degree this paper presents the existence criterions of solutions for the general nth-order differential equations under nonlinear boundary conditions and extends many existing results. Copyright 2006 Guangwa Wang et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction From Nagumo 10 there have been many accomplishments on the study of the existence of solutions for boundary value problems BVPs using the theory of differential inequality cf. 1-9 11-17 . However for the nth-order nonlinear differential equations with the nonlinear boundary conditions results are very few. The authors made some attempts to solve the nth-order Robin problem 14 . Now we are concerned with the nth-order nonlinear BVP y n f t y ý . y n-1 Pi y a y a . y n-1 a 0 i 1 . n - 1 Pn y b y b . y n-1 b 0 where t e I a b f t 0 1 . n-1 e C I X Rn R Pi n0 n1 . nn-1 e C Rn R Pn 0 Z1 . Zn-1 e c Rn R . Our method is not only modifying the nonlinear function in the original equations but also transforming the original nonlinear boundary conditions into some new boundary conditions which are easy to discuss. Thus we get the new BVP which will be discussed firstly then the judgement of the existence of solutions for the original BVP will be attained naturally. This technique dealing with the nonlinear problem is simpler and Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2006 Article ID 12040 Pages 1-12 DOI JIA 2006 12040 2 Differential inequalities method to nth-order BVPs clearer compared with the method of shooting. .

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