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Two-point boundary value problems for ordinary differential equations, uniqueness implies existence
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-20 , DOI: 10.1090/proc/15115
Paul W. Eloe , Johnny Henderson

Abstract:We consider a family of two-point $ n-1 ,1$ boundary value problems for $ n$th order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions that imply existence of solutions. A standard hypothesis that has proved effective in uniqueness implies existence type results is to assume uniqueness of solutions of a large family of $ n-$point boundary value problems. Here, we shall replace that standard hypothesis with one in which we assume uniqueness of solutions of a large family of two-point boundary value problems. We then obtain readily verifiable conditions on the nonlinear term that in fact imply the uniqueness of solutions of the large family of two-point boundary value problems.


中文翻译:

常微分方程的两点边值问题,唯一性意味着存在

摘要:我们考虑了三阶非线性常微分方程的一类两点$ n-1,1 $边值问题,$ n $并根据表示其存在的解的唯一性来获得条件。已证明在唯一性上有效的标准假设表示存在类型结果是假设一大类$ n- $点边界值问题的解的唯一性。在这里,我们将用一种假设代替标准假设,在该假设中,我们假设一大类两点边值问题的解的唯一性。然后,我们在非线性项上获得了易于验证的条件,该条件实际上暗示了两点边界值问题大家族的解的唯一性。
更新日期:2020-08-20
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