Existence of solutions in a cone for nonlinear alternative problems
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- by Juan J. Nieto PDF
- Proc. Amer. Math. Soc. 94 (1985), 433-436 Request permission
Abstract:
Using the alternative method we present sufficient conditions for the existence of positive solutions to nonlinear equations at resonance and extend a well-known result of Cesari and Kannan.References
- Lamberto Cesari, Functional analysis, nonlinear differential equations, and the alternative method, Nonlinear functional analysis and differential equations (Proc. Conf., Mich. State Univ., East Lansing, Mich., 1975) Lecture Notes in Pure and Appl. Math., Vol. 19, Marcel Dekker, New York, 1976, pp. 1–197. MR 0487630
- L. Cesari and R. Kannan, An abstract existence theorem at resonance, Proc. Amer. Math. Soc. 63 (1977), no. 2, 221–225. MR 448180, DOI 10.1090/S0002-9939-1977-0448180-3
- R. E. Gaines and Jairo Santanilla M., A coincidence theorem in convex sets with applications to periodic solutions of ordinary differential equations, Rocky Mountain J. Math. 12 (1982), no. 4, 669–678. MR 683861, DOI 10.1216/RMJ-1982-12-4-669
- N. G. Lloyd, Degree theory, Cambridge Tracts in Mathematics, No. 73, Cambridge University Press, Cambridge-New York-Melbourne, 1978. MR 0493564 J. J. Nieto, Positive solutions of operator equations, preprint 1984.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 433-436
- MSC: Primary 47A15; Secondary 35G20
- DOI: https://doi.org/10.1090/S0002-9939-1985-0787888-1
- MathSciNet review: 787888