Existence of solutions in a cone for nonlinear alternative problems

Nieto, Juan J.

doi:10.1090/S0002-9939-1985-0787888-1

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
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Positive solutions of operator equations