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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
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 
boundary value problems for 
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 
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边值问题，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
boundary value problems for 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 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
边值问题，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。
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