Boundary value problems for second and higher order differential equations
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- Proc. Amer. Math. Soc. 113 (1991), 761-775 Request permission
Abstract:
In this paper the nonlinear alternative of Leray-Schauder is used to obtain existence results for second and higher order boundary value problems.References
- A. R. Aftabizadeh, Chaitan P. Gupta, and Jian-Ming Xu, Existence and uniqueness theorems for three-point boundary value problems, SIAM J. Math. Anal. 20 (1989), no. 3, 716–726. MR 990873, DOI 10.1137/0520049
- L. E. Bobisud and Y. S. Lee, Existence for a class of nonlinear singular boundary value problems, Appl. Anal. 38 (1990), no. 1-2, 45–67. MR 1116175, DOI 10.1080/00036819008839954
- L. E. Bobisud, D. O’Regan, and W. D. Royalty, Singular boundary value problems, Appl. Anal. 23 (1986), no. 3, 233–243. MR 870490, DOI 10.1080/00036818608839643
- James Dugundji and Andrzej Granas, Fixed point theory. I, Monografie Matematyczne [Mathematical Monographs], vol. 61, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1982. MR 660439
- M. Frigon and D. O’Regan, On a generalization of a theorem of S. Bernstein, Ann. Polon. Math. 48 (1988), no. 3, 297–306. MR 978681, DOI 10.4064/ap-48-3-297-306
- Andrzej Granas, Ronald Guenther, and John Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. (Rozprawy Mat.) 244 (1985), 128. MR 808227
- A. Granas, R. B. Guenther, and J. W. Lee, Existence principles for classical and Carathéodory solutions of nonlinear systems and applications, Differential equations and applications, Vol. I, II (Columbus, OH, 1988) Ohio Univ. Press, Athens, OH, 1989, pp. 353–364. MR 1026162 —, Some general existence principles in the Carathéodory theory of nonlinear differential equations J. Math. Pure Appl. (to appear).
- Chaitan P. Gupta, Existence and uniqueness theorems for the bending of an elastic beam equation, Appl. Anal. 26 (1988), no. 4, 289–304. MR 922976, DOI 10.1080/00036818808839715
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
- Dang Dinh Hai, Existence and uniqueness of solutions for a nonlinear second order differential equation in Hilbert space, Proc. Edinburgh Math. Soc. (2) 33 (1990), no. 1, 89–95. MR 1038768, DOI 10.1017/S0013091500028911
- John W. Lee and Donal O’Regan, Existence of solutions to some initial value, two-point, and multi-point boundary value problems with discontinuous nonlinearities, Appl. Anal. 33 (1989), no. 1-2, 57–77. MR 1013453, DOI 10.1080/00036818908839861 D. O’Regan, Second and higher order systems of boundary value problems, J. Math. Anal. Appl. (to appear).
- Yi Song Yang, Fourth-order two-point boundary value problems, Proc. Amer. Math. Soc. 104 (1988), no. 1, 175–180. MR 958062, DOI 10.1090/S0002-9939-1988-0958062-3
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 761-775
- MSC: Primary 34B15; Secondary 47H15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1069295-2
- MathSciNet review: 1069295