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Existence and uniqueness of solutions of boundary value problems for Lipschitz equations. (English) Zbl 0407.34018


MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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References:

[1] Hartman, P., On \(n\)-parameter families and interpolation problems for nonlinear ordinary differential equations, Trans. Amer. Math. Soc., 154, 201-226 (1971) · Zbl 0222.34017
[2] Klaasen, G., Existence theorems for boundary value problems for \(n\) th order ordinary differential equations, Rocky Mtn. J. Math., 3, 457-472 (1973) · Zbl 0268.34025
[3] Hartman, P., Unrestricted \(n\)-parameter families, Rend. Circ. Mat. Palermo (2), 7, 123-142 (1958) · Zbl 0085.04505
[4] Melentsova, Y.; Milshtein, H., An optimal estimate of the interval on which a multipoint boundary value problem possesses a solution, Differencial’nye Uravrnenija, 10, 1630-1641 (1974) · Zbl 0314.34028
[5] Lee, E.; Markus, L., Foundations of Optimal Control Theory (1967), Wiley: Wiley New York · Zbl 0159.13201
[6] Peterson, A., Comparison theorems and existence theorems for ordinary differential equations, J. Math. Anal. Appl., 55, 773-784 (1976) · Zbl 0342.34008
[7] Hinton, D., Disconjugate properties of a system of differential equations, J. Differential Equations, 2, 420-437 (1966) · Zbl 0161.27904
[8] Agarwal, R.; Krishnamurthy, P., On the uniqueness of solutions of nonlinear boundary value problems, J. Math. Phys. Sci., 10, 17-31 (1976) · Zbl 0328.34012
[9] Sherman, T., Properties of solutions of \(n\) th order linear equations, Pacific J. Math., 15, 1045-1060 (1965) · Zbl 0132.31204
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