Existence results for some initial and boundary value problems without growth restriction
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- by Marlène Frigon and Donal O’Regan PDF
- Proc. Amer. Math. Soc. 123 (1995), 207-216 Request permission
Abstract:
In this paper, using the Schauder Fixed Point Theorem, we establish some existence results or initial and boundary value problems for differential equations withouth growth restriction on the right member.References
- Alberto Cabada, The monotone method for first-order problems with linear and nonlinear boundary conditions, Appl. Math. Comput. 63 (1994), no. 2-3, 163–186. MR 1280536, DOI 10.1016/0096-3003(94)90193-7
- James Dugundji and Andrzej Granas, Fixed point theory. I, Monografie Matematyczne [Mathematical Monographs], vol. 61, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1982. MR 660439
- Marlène Frigon, Théorèmes d’existence pour des problèmes aux limites sans condition de croissance, Bull. Sci. Math. 117 (1993), no. 3, 377–400 (French, with English and French summaries). MR 1228951
- M. Frigon and D. O’Regan, Some general existence principles for ordinary differential equations, Topol. Methods Nonlinear Anal. 2 (1993), no. 1, 35–54. MR 1245477, DOI 10.12775/TMNA.1993.029
- Andrzej Granas, Ronald Guenther, and John Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. (Rozprawy Mat.) 244 (1985), 128. MR 808227
- M. N. Nkashama, A generalized upper and lower solutions method and multiplicity results for nonlinear first-order ordinary differential equations, J. Math. Anal. Appl. 140 (1989), no. 2, 381–395. MR 1001864, DOI 10.1016/0022-247X(89)90072-3
- Anthony G. O’Farrell and Donal O’Regan, Existence results for some initial and boundary value problems, Proc. Amer. Math. Soc. 110 (1990), no. 3, 661–673. MR 1021212, DOI 10.1090/S0002-9939-1990-1021212-6
- L. C. Piccinini, G. Stampacchia, and G. Vidossich, Ordinary differential equations in $\textbf {R}^{n}$, Applied Mathematical Sciences, vol. 39, Springer-Verlag, New York, 1984. Problems and methods; Translated from the Italian by A. LoBello. MR 740539, DOI 10.1007/978-1-4612-5188-0
- Armando Rodriguez and Antonio Tineo, Existence theorems for the Dirichlet problem without growth restrictions, J. Math. Anal. Appl. 135 (1988), no. 1, 1–7. MR 960802, DOI 10.1016/0022-247X(88)90137-0
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 207-216
- MSC: Primary 34B15; Secondary 34A12, 47H15, 47N20
- DOI: https://doi.org/10.1090/S0002-9939-1995-1233971-2
- MathSciNet review: 1233971