Contractive mappings and periodically perturbed conservative systems

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1. Sh. Ahmad, An existence theorem for periodically perturbed conservative systems, Michigan Math. J. 20 (1973) 385-392. (1973) Zbl0294.34029MR0346246
2. S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math. 3 (1922) 133-181. (1922) 
3. L. Cesari, Alternative methods in nonlinear analysis, Proc. Int. Conf. Differential Equations, Los Angeles, Sept. 74, Academic Press, 1975, 95-148. (1975) Zbl0316.47039MR0430884
4. C. L. Dolph, Non-linear integral equations of the Hammerstein type, Trans. Amer. Math. Soc. 66 (1949) 289-307. (1949) MR0032923
5. H. Ehrmann, On implicit function theorems and the existence of solutions of non-linear equations, L'Enseignement Math. 9 (1963) 129-176. (1963) Zbl0127.08004MR0156175
6. H. Ehrmann, H. E. Lahmann, Anwendungen des Schauderschen Fixpunktsatzes auf gewisse nichtlineare Integralgleichungen, L'Enseignement Math. 11 (1965) 267-280. (1965) Zbl0196.13002MR0202013
7. M. Golomb, Zur Theorie der nichtlinearen Integralgleichungen, Integralgleichungssysteme und allgemeinen Funktionalgleichungen, Math. Z. 39 (1935) 45-75. (1935) MR1545488
8. J. K. Hale, Applications of alternative problems, Brown Univ. Lecture Notes 71-1, Providence, RI, 1971. (1971) 
9. A. Hammerstein, Nichtlineare Integralgleichungen nebst Anwendungen, Acta Math. 54 (1930) 117-176. (1930) MR1555304
10. R. Kannan, Periodically perturbed conservative systems, J. Differential Equations, 16 (1974) 506-514. (1974) Zbl0349.34029MR0417493
11. T. Kato, Perturbation theory for linear operators, Springer, Berlin, 1966. (1966) Zbl0148.12601
12. I. Kolodner, Equations of Hammerstein type in Hilbert spaces, J. Math. Mech. 13 (1964) 701-750. (1964) Zbl0149.36401MR0171184
13. A. C. Lazer, D. A. Sanchez, On periodically perturbed conservative systems, Michigan Math. J. 16 (1969) 193-200. (1969) Zbl0187.34501MR0245906
14. A. C. Lazer, Application of a lemma on bilinear forms to a problem in nonlinear oscillations, Proc. Amer. Math. Soc. 33 (1972) 89-94. (1972) Zbl0257.34041MR0293179
15. D. E. Leach, On Poincaré's perturbation theorem and a theorem of W. S. Loud, J. Differential Equations 7 (1970) 34-53. (1970) Zbl0186.15501MR0251308
16. W. S. Loud, Periodic solutions of nonlinear differential equations of Duffing type, Proc. U.S.-Japan Semin. on Diff. and Funct. Equations, Benjamin, New York, 1967, 199-224. (1967) Zbl0162.12302MR0223656
17. N. Rouche, J. Mawhin, Equations différentielles ordinaires, vol. 1, Masson, Paris, 1973. (1973) Zbl0289.34001MR0481182
18. M. M. Vainberg, Variational method and method of monotone operators in the theory of nonlinear equations, Wiley, New York, 1973. (1973) Zbl0279.47022MR0467428

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