An existence theorem for nonlinear boundary value problems

Authors:
Keith Schrader and Paul Waltman

Journal:
Proc. Amer. Math. Soc. **21** (1969), 653-656

MSC:
Primary 34.36

DOI:
https://doi.org/10.1090/S0002-9939-1969-0239176-0

MathSciNet review:
0239176

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References | Similar Articles | Additional Information

**[1]**P. B. Bailey and L. F. Shampine,*Existence from uniqueness for two point boundary value problems*, J. Math. Anal. Appl. (to appear). MR**0239173 (39:530)****[2]**L. Jackson, ``Subfunctions and second order differential inequalities'' in*Advances in mathematics*, Academic Press, New York, 1968, pp. 307-363. MR**0229896 (37:5462)****[3]**E. Kamke,*Zur Theorie der Systeme gewöhnlicher Differentialgleichungen*. II, Acta. Math.**58**(1932), 57-85. MR**1555344****[4]**A. Lasota and Z. Opial,*On the existence and uniqueness of solutions of a boundary value problem for an ordinary differential equation*, Colloq. Math.**18**(1967), 1-5. MR**0219792 (36:2871)****[5]**K. Schrader,*Existence theorems for second order boundary value problems*, J. Differential Equations (to appear). MR**0239175 (39:532)****[6]**G. R. Sell,*On the fundamental theory of ordinary differential equations*, J. Differential Equations**1**(1965), 370-392. MR**0176130 (31:405)****[7]**L. Shampine,*Existence and uniqueness for nonlinear boundary value problems*, J. Differential Equations (to appear). MR**0239177 (39:534)****[8]**T. L. Sherman,*Uniqueness for second order boundary value problems*, J. Differential Equations (to appear). MR**0247174 (40:443)****[9]**P. Waltman,*Existence and uniqueness of solutions to a nonlinear boundary value problem*, J. Math. Mech.**18**(1968), 585-586. MR**0235193 (38:3504)****[10]**T. Yoshizawa,*Stability theory by Liapunov's second method*, Publ. Math. Soc. Japan, No. 9, Tokyo, 1966. MR**0208086 (34:7896)**

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DOI:
https://doi.org/10.1090/S0002-9939-1969-0239176-0

Article copyright:
© Copyright 1969
American Mathematical Society