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Báo cáo hóa học: " Research Article On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients"

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: Research Article On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 384910 16 pages doi 10.1155 2008 384910 Research Article On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients Vita Pylypenko1 and Andras Ronto2 1 National Technical University of Ukraine Kyiv Polytechnic Institute Faculty of Physics and Mathematics 37 Peremohy Avenue 03 056 Kyiv Ukraine 2 Institute of Mathematics Academy of Sciences of Czech Republic Zizkova 22 61662 Brno Czech Republic Correspondence should be addressed to Andras Ronto ronto@math.cas.cz Received 26 May 2008 Accepted 1 September 2008 Recommended by Alberto Cabada The problem on solutions with specified growth for linear functional differential equations with negative coefficients is treated by using two-sided monotone iterations. New theorems on the existence and localisation of such solutions are established. Copyright 2008 V. Pylypenko and A. Ronto. 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. Problem setting and introduction In this paper we are concerned with the problem on the existence and localisation of solutions of singular linear functional differential equations. The class of equations under examination comprises in particular the differential equation with argument deviations n u t 2Pk t u wk 0 f t t e a b 1.1 k 0 considered together with the additional condition sup h t u t x 1.2 te a b where h a b R is a certain given continuous nondecreasing function such that h t 0 for t e a b and lim h t 0. 1.3 t a 2 Journal of Inequalities and Applications The argument deviations in 1.1 are given by arbitrary Lebesgue measurable functions Wk k 0 1 . n transforming the interval a b to itself this setting does not lead one to any loss of generality see e.g. 1 . We are interested in conditions .