×

Uniqueness for second order nonlinear boundary value problems with applications to almost periodic solutions. (English) Zbl 0195.09802


Full Text: DOI

References:

[1] Amerio, L., Soluzioni quasi-periodiche, o limitate di sistemi differenziali non lineari quasi-periodici o limitati, Ann. Mat. Pura Appl., 39, 97-119 (1955) · Zbl 0066.07202 · doi:10.1007/BF02410765
[2] Bailey, P.; Shampine, L. F.; Waltman, P., The first and second boundary value problems for non-linear second order differential equations, J. of Diff. Eqtns., 2, 399-411 (1966) · Zbl 0145.11104 · doi:10.1016/0022-0396(66)90050-7
[3] Bailey, P.; Waltman, P., On the distance between consecutive zeros for second order differential equations, J. Math. Analysis and App., 14, 23-30 (1966) · Zbl 0142.34703 · doi:10.1016/0022-247X(66)90058-8
[4] Bailey, P.; Waltman, P., Existence and uniqueness of solutions of the first boundary value problem for nonlinear second order differential equations, Archive for Rational Mechanics and Analysis, 21, 310-320 (1966) · Zbl 0152.08602 · doi:10.1007/BF00282251
[5] Bebernes, J. W.; Jackson, L. K., Infinite interval boundary value problems for y″ = f(x, y), Duke Math. J., 34, 39-48 (1967) · Zbl 0145.33102 · doi:10.1215/S0012-7094-67-03404-7
[6] Caccioppoli, R., Problemi non lineari in analisi funzionale, Rend. Sem. Math. di Roma, 1, 3, 13-22 (1933) · Zbl 0008.36003
[7] Coles, W. J.; Sherman, T. L., Convergence of successive approximations for nonlinear two-point boundary value problems, SIAM J. Appl. Math., 15, 426-433 (1967) · Zbl 0154.40802 · doi:10.1137/0115038
[8] – –, and – –,Two-point problems for non-linear second order ordinary differential equations, Report 513 (Math. Researh Center, Univ. of Wiscosin, 1964).
[9] Ebert, A., On the zeros of the solutions of the differential equation y″ + q(x)y = 0, where [q(x)]^v is concave, Studia Scient. Math. Hung., 2, 293-298 (1967) · Zbl 0161.27801
[10] Fink, A. M., Uniqueness theorems and almost periodic solutions to second order differential equations, J. Diff. Eqtns., 4, 543-548 (1968) · Zbl 0167.38303 · doi:10.1016/0022-0396(68)90004-1
[11] – –,Almost automorphic and almost periodic solutions which minimize functionals, to appear. · Zbl 0177.12102
[12] Groppi, I., A proposito di alcuni criteri di confronto per le equazioni differenziali del secondo ordine, Boll. Un. Mat. Ital., 17, 179-182 (1938) · JFM 64.0441.02
[13] Hartman, P.; Wintner, A., On an oscillation criterion of Liapounoff, Amer. J. Math., 73, 885-890 (1951) · Zbl 0043.08704
[14] Hartman, P.; Wintner, A., An equality for the first eigenvalue of an ordinary boundary value problem, Quarterly Applied Math., 13, 324-326 (1955) · Zbl 0065.31803
[15] Levin, A. Ju., Linear differential equations of second order, Dokl. Akad. Nauk SSSR, 153, 1257-1260 (1963) · Zbl 0128.30901
[16] Opial, Z., Sur une inégalité de C. de la Vallée Poussin dans la théorie de l’équation différentielle linéaire du second ordre, Ann. Polon. Math., 6, 87-91 (1959) · Zbl 0084.08103
[17] Petrov, V. N., The limits of applicability of S. Tchaplygin’s theorem on differential inequalities for linear equations with derivatives of the second order, C. R. (Doklady) Akad. Nauk Sci. URSS (N. S.), 51, 255-258 (1946) · Zbl 0061.19501
[18] Rab, M., Kriterien für die oszillation der Lösungen der Differentialgleichung [p(x)y′]′ + + q(x)y=0, Casopis pro pest. mat., 84, 335-368 (1959) · Zbl 0087.29505
[19] Rosenblatt, A., Sur les problémes aux limites des équations differentielles ordinaires du second ordre, Bull. Soc. Roy. Sci. Liége, 2, 87-89 (1933) · Zbl 0007.01101
[20] Rosenblatt, A., Sur les théorèmes de M. Picard dans la théorie des problèms aux limites des. équations différentielles ordinaires non-linéaires, Bull, Sci. Math., 57, 100-106 (1933) · JFM 59.0448.02
[21] Sansone, G., Equazioni Differenziali nel Campo Reale (1949), Bologna: Nicola Zanichelli, Bologna · Zbl 0039.30901
[22] K. Schmitt,Bounded solutions of nonlinear second order differentail equations, Duke Math. J., to appear.
[23] Schrader, K. W., Boundary - Value problems for second - order ordinary differential equations, J. of Diff. Eqtns., 3, 403-413 (1967) · Zbl 0152.28401 · doi:10.1016/0022-0396(67)90040-X
[24] – –,A note on second order differential inequalities, Proc. Amer. Math. Soc, 19 (1968) · Zbl 0164.39404
[25] – –,Solutions of second order ordinary differential equations, J. Diff. Eqtns., 4 (1968). · Zbl 0174.13503
[26] Seifert, G., Some recent results for almost periodic solutions of differential equations, SIAM Review, 7, 529-538 (1965) · Zbl 0131.08603 · doi:10.1137/1007109
[27] Trevisan, G., Teoremi di unicità e confronto per problemi relativi a sistemi di due equazioni differenziali ordinarie del primo ordine, Rend. Sem. Mat. Univ. Padova, 12, 12-21 (1941) · JFM 67.0321.03
[28] Trevisan, G., Un teorema per i sistemi di due equazioni differenziali ordinarie, Rend. Sem. Math. Univ. Padova, 17, 219-221 (1949) · Zbl 0031.21402
[29] Wilkins, J. E. Jr., The converse of a theorem of Tchaplygin on differential inequalities, Bull. Amer. Ma. Soc., 53, 126-129 (1947) · Zbl 0031.39701 · doi:10.1090/S0002-9904-1947-08759-0
[30] Willett, D., Uniqueness of solutions of boundary value problems, SIAM Review, 9, 726-728 (1967) · Zbl 0173.10301 · doi:10.1137/1009114
[31] – –,On the oscillatory behaviour of the solutions of second order linear differential equations, Annales Polonici Mat., 21 (1968).
[32] Zaidman, S., Evalutations de la distance entre les zéros des solutions des équations différentielles, Rev. Univ. « C. I. Parhon » Politehn. Bucuresti. Ser. Sti. Nat., 4, 6-7, 47-54 (1955) · Zbl 0067.06201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.