Boundary value problems for first-order differential equations
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- by L. E. Bobisud and D. O’Regan PDF
- Proc. Amer. Math. Soc. 99 (1987), 501-506 Request permission
Abstract:
Conditions sufficient to guarantee existence and uniqueness of solutions to multipoint boundary value problems for the first-order differential equation $y’ = h(t,y)$ are given when $h$ fails to be Lipschitz along a solution of $y’ = h(t,y)$ and the initial-value problem thus has nonunique solutions.References
- Paul B. Bailey, Lawrence F. Shampine, and Paul E. Waltman, Nonlinear two point boundary value problems, Mathematics in Science and Engineering, Vol. 44, Academic Press, New York-London, 1968. MR 0230967
- C. Bandle, R. P. Sperb, and I. Stakgold, Diffusion and reaction with monotone kinetics, Nonlinear Anal. 8 (1984), no. 4, 321–333. MR 739663, DOI 10.1016/0362-546X(84)90034-8
- Lloyd K. Jackson, Existence and uniqueness of solutions of boundary value problems for Lipschitz equations, J. Differential Equations 32 (1979), no. 1, 76–90. MR 532764, DOI 10.1016/0022-0396(79)90052-4 V. Lakshmikantham and S. Leela, Differential and integral inequalities: Theory and applications, vol. 1, Academic Press, New York, 1969.
- Atsushi Yoshikawa, On a simple singular perturbation problem, J. Differential Equations 60 (1985), no. 3, 363–380. MR 811772, DOI 10.1016/0022-0396(85)90130-5
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 501-506
- MSC: Primary 34B10; Secondary 34A10, 34B15
- DOI: https://doi.org/10.1090/S0002-9939-1987-0875388-1
- MathSciNet review: 875388