tailieunhanh - báo cáo hóa học: " On singular nonlinear distributional and impulsive initial and 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: On singular nonlinear distributional and impulsive initial and boundary value problems | Heikkilă Boundary Value Problems 2011 2011 24 http content 2011 1 24 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access On singular nonlinear distributional and impulsive initial and boundary value problems Seppo Heikkila Correspondence sheikki@ Department of Mathematical Sciences University of Oulu BOX 3000 FIN-90014 Oulu Finland Springer Abstract Purpose To derive existence and comparison results for extremal solutions of nonlinear singular distributional initial value problems and boundary value problems. Main methods Fixed point results in ordered function spaces and recently introduced concepts of regulated and continuous primitive integrals of distributions. Maple programming is used to determine solutions of examples. Results New existence results are derived for the smallest and greatest solutions of considered problems. Novel results are derived for the dependence of solutions on the data. The obtained results are applied to impulsive differential equations. Concrete examples are presented and solved to illustrate the obtained results. MSC 26A24 26A39 26A48 34A12 34A36 37A37 39B12 39B22 47B38 47J25 47H07 47H10 58D25 Keywords distribution primitive integral regulated continuous initial value problem boundary value problem singular distributional 1 Introduction In this paper existence and comparison results are derived for the smallest and greatest solutions of first and second order singular nonlinear initial value problems as well as second order boundary value problems. Recently similar problems are studied in ordered Banach spaces . in 1-4 by converting problems into systems of integral equations integrals in these systems being Bochner-Lebesgue or Henstock-Kurzweil integrals. A novel feature in the present study is that the right-hand sides of the considered differential equations comprise distributions on a compact real interval a b . Every distribution is assumed to have a primitive in the

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