Ordinary differential equations with nonlinear boundary conditions. (English) Zbl 0326.34021


34B15 Nonlinear boundary value problems for ordinary differential equations
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[1] Avramescu, C.: Sisteme diferentiale cu conditii la limita generale. Bul. inst. Politehn. iasi 11, 35-42 (1965)
[2] Bebernes, J. W.; Wilhelmsen, R.: A technique for solving two-dimensional boundary value problems. SIAM J. Appl. math. 17, 1060-1064 (1969) · Zbl 0212.17703
[3] Bebernes, J. W.; Wilhemsen, R.: A general boundary value technique. J. differential equations 8, 404-415 (1970) · Zbl 0211.39904
[4] Bebernes, J. W.; Wilhelmsen, R.: A remark concerning a boundary value problem. J. differential equations 10, 389-391 (1971) · Zbl 0268.34026
[5] Bernfeld, S.; Lakshmikantham, V.: Existeàce of solutions of ordinary differential equations with generalized boundary conditons. Trans. amer. Math. soc. 184, 261-274 (1973) · Zbl 0276.34013
[6] Bernfeld, S.; Lakshmikantham, V.: An introduction to nonlinear boundary value problems. (1974) · Zbl 0286.34018
[7] Conti, R.: Recent trends in the theory of boundary value problems for ordinary differential equations. Boll. un. Mat. ital. 22, 135-178 (1967) · Zbl 0154.09101
[8] Erbe, L. H.: Nonlinear boundary value problems for second-order differential equations. J. differential equations 7, 459-472 (1970) · Zbl 0284.34017
[9] Gaines, R. E.; Mawhin, J.: Coincidence degree and nonlinear differential equations. Lecture notes in mathematics, 568 (1977) · Zbl 0339.47031
[10] Gudkov, V. V.; Lepin, Ya: The solvability of certain boundary-value problems for ordinary second-order differential equations. Differncial’nye uravnenija 7, 1779-1788 (1971)
[11] Gudkov, V. V.; Lepin, A. Ya: On necessary and sufficient conditions for the solvability of certain boundary value problems for a second-order ordinary differential equation. Dokl. akad. Nauk SSSR 210 (1973) · Zbl 0289.34022
[12] Hartman, P.: On boundary value problems for systems of ordinary nonlinear second-order differential equations. Trans. amer. Math. soc. 96, 493-509 (1960) · Zbl 0098.06101
[13] Hartman, P.: Ordinary differential equations. (1964) · Zbl 0125.32102
[14] Jackson, L. K.; Klaasen, G.: A variation of the topological method of wazewsky. SIAM J. Appl. math. 20, 124-130 (1971) · Zbl 0231.34007
[15] Krasnosel’skii, M. A.; Lifshitz, E. A.: Duality principles for boundary value problems for nonlinear systems. Soviet math. Dokl. 8, 1236-1239 (1967) · Zbl 0176.04902
[16] Mawhin, J.: Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces. J. differential equations 12, 610-636 (1972) · Zbl 0244.47049
[17] Mawhin, J.: A further invariance property of coincidence degree in convex spaces. Am. soc. Sci. bruxelles 87, 51-57 (1973) · Zbl 0252.47070
[18] Mawhin, J.: Nonlinear perturbations of Fredholm mappings in normed spaces and applications to differential equations. Univ. de brasilia, trabalho de matem., no. 61 (1974) · Zbl 0334.34007
[19] Mawhin, J.: Recent trends in nolinear boundary value problems. Proceedings VII intern. Conf. nonlinear oscillations (September 1975)
[20] Mazzone, S.: Un caso di unicita per problemi ai limiti non lineari reletivi ad equazioni differenziali del secondo ordine. Rend. soc. Sci. lettere napoli, 97-101 (1971)
[21] Muldowney, J. S.; Willett, D.: An elementary proof of the existence of solutions to second-order nonlinear boundary value problems. SIAM J. Math. anal. (1974) · Zbl 0285.34012
[22] Rouche, N.; Mawhin, J.: Equations differentielles ordinaires. (1973) · Zbl 0289.34001
[23] Schmitt, K.: Randwertaufgaben fur gewöhnliche differentialgleichungen. Proceed. streiermonk. Math. sympos. Graz (1973) · Zbl 0276.34012
[24] Stampacchia, G.: Sulle condizioni che determinano gli integrali dei, un sistemi di due equazioni differenziali ordinarie del primo ordine. Atti. accad. Naz. lincei rend. Cl. sci. Fis. mat. Natur. 2, 411-418 (1947) · Zbl 0029.26101
[25] Stampacchia, G.: Sulle condizioni che determinano gli integrali dei sistemi di equazioni differenziali ordinarie del primo ordine. Giern. mat. Battaglini 77, 55-60 (1947) · Zbl 0029.26101
[26] Stampacchia, G.: Sopra una generalizzazione dei problemi ai limiti per i sistemi di equazioni differenziali ordinarie. Ric. mat. 3, 76-94 (1954) · Zbl 0056.31302
[27] Waltman, P.: Existence and uniqueness of solutions of boundary value problels for two-dimensional systems of nonlinear differential equations. Tran. amer. Math. soc. 153, 223-234 (1971) · Zbl 0228.34016
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