Lovelady: Convergent solutions of nonlinear differential equations

Lovelady, David Lowell:
Convergent solutions of nonlinear differential equations
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 54 (1973), fasc. n.2, p. 193-198, (English)
pdf (467 Kb), djvu (632 Kb). | MR 0355240 | Zbl 0307.34062

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Sono date condizioni sufficienti che assicurano che se $f$ è convergente allora ogni soluzione $v(t)$ dell'equazione $v'(t) = f)t) + F(t,v(t))$ è convergente. Questi risultati sono applicati per scegliere $\lim_{t \to \infty} v(t)$. Soluzioni convergenti sono pure ottenute per l'equazione perturbata $u'(t) = f(t) + F(t,u(t)) + G(t,u(t))$.

Referenze Bibliografiche

[1] F. BRAUER, Global behavior of solutions of ordinary differential equations, «J. Math. Anal. Appl.», 2, 145-158 (1961). | fulltext (doi) | MR 130423 | Zbl 0101.30305

[2] F. BRAUER, Bounds for solutions of ordinary differential equations, «Proc. Amer. Math. Soc.», 14, 36-43 (1963). | fulltext (doi) | MR 142829 | Zbl 0113.06803

[3] W. A. COPPEL, Stability and asymptotic behavior of differential equations, D. C. Heath & Co., Boston 1965. | MR 190463 | Zbl 0154.09301

[4] T. G. HALLAM, A terminal comparison principle for differential inequalities, «Bull. Amer. Math. Soc.», 78, 230-233 (1972). | fulltext (doi) | MR 288396 | Zbl 0243.34018

[5] T. G. HALLAM, Convergence of solutions of nonlinear differential equations, «Ann. Mat. Pura Appl.», to appear. | fulltext (doi) | MR 315233 | Zbl 0283.34052

[6] T. G. HALLAM and J. W. HEIDEL, The asymptotic manifolds of a perturbed linear system of differential equations, «Trans. Amer. Math. Soc.», 149, 233-241 (1970). | fulltext (doi) | MR 257486 | Zbl 0186.41502

[7] T. G. HALLAM, G. LADAS and V. LAKSHMIKANTHAM, On the asymptotic behavior of functional differential equations, «SIAM J. Math. Anal.», 3, 58-64 (1972). | fulltext (doi) | MR 315247 | Zbl 0241.34078

[8] T. G. HALLAM and V. LAKSHMIKANTHAM, Growth estimates for convergent solutions of ordinary differential equations, «J. Math. Phys. Sci.», 5, 83-88 (1971). | MR 298127 | Zbl 0231.34026

[9] V. LAKSHMIKANTHAM and S. LEELA, Differential and integral inequalities, vol. 1, Academic Press, New York 1969. | MR 379933 | Zbl 0177.12403

[10] D. L. LOVELADY, A functional differential equation in a Banach space, «Funkcialaj Ekvacioj», 14, 111-122 (1971). | MR 304754 | Zbl 0231.45016

[11] D. L. LOVELADY, Asymptotic equivalence for two nonlinear systems, «Math. Systems Theory», 7, 170-175 (1973). | fulltext (doi) | MR 320454 | Zbl 0258.34037

[12] D. L. LOVELADY, Global attraction and asymptotic equilibrium for nonlinear ordinary equations, Conference on the theory of ordinary and partial differential equations, pp. 303-307, «Lecture Notes Math.», 280, Springer-Verlag, New York 1972. | MR 425289

[13] D. L. LOVELADY and R. H. MARTIN, Jr., A global existence theorem for an ordinary differential equation in a Banach space, «Proc. Amer. Math. Soc.», 35, 445-449 (1972). | fulltext (doi) | MR 303035

[14] S. M. LOZINSKII, Error estimates for the numerical integration of ordinary differential equations I, «Isv. Vyss. Ucebn. Zaved. Mat.», (5) 6, 52-90 (1958) (Russian). | MR 145662 | Zbl 0198.21202

[15] J. D. MAMEDOV, One-sided estimates in the conditions for existence and uniqueness of solutions of the limit Cauchy problem in a Banach space, «Sibirsk. Mat. Ž.», 6, 1190-1196 (1965) (Russian). | MR 190496 | Zbl 0173.43501

[16] R. H. MARTIN, Jr., A global existence theorem for autonomous differential equations in a Banach space, «Proc. Amer. Math. Soc.», 26, 307-314 (1970). | fulltext (doi) | MR 264195

[17] N. PAVEL, Sur certaines équations differentielles abstraites, «Boll. Un. Mat. Ital.», to appear. | MR 342807

[18] T. WAŽEWSKI, Sur la limitation des integrales des systèmes d'équations différentielles linéaires ordinaires, «Studia Math.», 10, 48-59 (1948). | fulltext EuDML | fulltext (doi) | MR 25651 | Zbl 0036.05703

[19] A. WINTNER, Asymptotic equilibria, «Amer. J. Math.», 68, 125-132 (1946). | fulltext (doi) | MR 14529 | Zbl 0063.08289

[20] A. WINTNER, An Abelian lemma concerning asymptotic equilibria, «Amer. J. Math.», 68, 451-454 (1946). | fulltext (doi) | MR 16812 | Zbl 0063.08294

[21] A. WINTNER, On a theorem of Bocher in the theory of ordinary linear differential equations, «Amer. J. Math.», 76, 183-190 (1954). | fulltext (doi) | MR 58800 | Zbl 0055.08104

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Referenze Bibliografiche