Constructive analysis of periodic solutions with interval halving

Boundary value problems

Mikls Ront¹  Andrs Ront²  Nataliya Shchobak⁴ 

[1] Department of Analysis, University of Miskolc, EgyetemváInstitute of Mathematics, Academy of Sciences of Czech Republic, Brno, Czech Republic;Uzhgorod National University, Uzhgorod, Ukraine;ros, Miskolc, Hungary

关键词: periodic solution;    periodic boundary value problem;    parametrisation;    periodic successive approximations;    numerical-analytic method;    interval halving;    existence;    continuation;    Mawhin’s theorem;   

DOI  :  10.1186/1687-2770-2013-57

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

For a constructive analysis of the periodic boundary value problem for systems of non-linear non-autonomous ordinary differential equations, a numerical-analytic approach is developed, which allows one to both study the solvability and construct approximations to the solution. An interval halving technique, by using which one can weaken significantly the conditions required to guarantee the convergence, is introduced. The main assumption on the equation is that the non-linearity is locally Lipschitzian. An existence theorem based on properties of approximations is proved. A relation to Mawhin’s continuation theorem is indicated. MSC:34B15.

【 授权许可】

CC BY