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Uniqueness implies existence and uniqueness conditions for a class of (k + j)-point boundary value problems for nth order differential equations

机译:唯一性暗示n阶微分方程的一类(k + j)点边值问题的存在性和唯一性条件

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For the nth order nonlinear differential equation, y(n) = f(x, y, y′, …, y(n−1)), we consider uniqueness implies existence results for solutions satisfying certain (k + j)-point boundary conditions, 1 ⩽ j ⩽ n − 1, and 1 ⩽ k ⩽ n − j. We define (k; j)-point unique solvability in analogy to k-point disconjugacy and we show that (n − j0; j0)-point unique solvability implies (k; j)-point unique solvability for 1 ⩽ j ⩽ j0, and 1 ⩽ k ⩽ n − j. This result is in analogy to n-point disconjugacy implies k-point disconjugacy, 2 ⩽ k ⩽ n − 1. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
机译:对于n阶非线性微分方程y (n) = f(x,y,y',…,y (n-1)),我们认为唯一性意味着满足某些(k + j)点边界条件1⩽j⩽n-1和1⩽k⩽n-j的解的存在结果。我们定义(k; j)点唯一可解性,类似于k点不相容性,我们证明(n − j 0 ; j 0 )点唯一可解性意味着(k; j)点对于1⩽j 0 和1⩽n − j的唯一可解性。该结果类似于n点不一致性,暗示k点不一致性,2 k n −1。©2011 WILEY-VCH Verlag GmbH&Co. KGaA,Weinheim

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