tailieunhanh - Báo cáo hóa học: " Existence of positive solutions to periodic boundary value problems with sign-changing Green’s function"

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: Existence of positive solutions to periodic boundary value problems with sign-changing Green’s function | Zhong and An Boundary Value Problems 2011 2011 8 http content 2011 1 8 0 Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Existence of positive solutions to periodic boundary value problems with sign-changing Green s function Shengren Zhong1 and Yukun An2 Correspondence anykna@nuaa. department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016 PR China Full list of author information is available at the end of the article Abstract This paper deals with the periodic boundary value problems i u p2u f u 0 t T u 0 u T u 0 u T where 0 p 2t is a constant and in which case the associated Green s function may changes sign. The existence result of positive solutions is established by using the fixed point index theory of cone mapping. Keywords periodic boundary value problem positive solution sign-changing Green s function cone fixed point theorem 1 Introduction The periodic boundary value problems i u a t u f t u 0 t T ị u 0 u T u 0 u T 1 where f is a continuous or L1-Caratheodory type function have been extensively studied. A very popular technique to obtain the existence and multiplicity of positive solutions to the problem is Krasnosel skii s fixed point theorem of cone expansion compression type see for example 1-4 and the references contained therein. In those papers the following condition is an essential assumptions A The Green function G t s associated with problem 1 is positive for all t s e 0 T X 0 n Under condition A Torres get in 4 some existence results for 1 with jumping nonlinearities as well as 1 with a repulsive or attractive singularity and the authors in 3 obtained the multiplicity results to 1 when ft u has a repulsive singularity near x 0 andf t u is super-linear near x . In 2 a special case a t m2 and m e 0 T was considered the multiplicity results to 1 are obtained when the nonlinear term ft u is singular at u 0 and is super-linear at u . Recently in 5 the .

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