Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on disconjugate differential equations and growth estimates


Author: L. Erbe
Journal: Proc. Amer. Math. Soc. 83 (1981), 85-90
MSC: Primary 34C11; Secondary 34A40
DOI: https://doi.org/10.1090/S0002-9939-1981-0619988-7
MathSciNet review: 619988
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Subfunctions and differential inequality techniques are applied to certain classes of second and third order nonlinear equations to obtain growth estimates on the solutions.


References [Enhancements On Off] (What's this?)

  • [1] G. Anichini and J. D. Schuur, Using a fixed point theorem to describe the asymptotic behavior of solutions of a class of nonlinear ordinary differential equations, (Proc. Conf. Equadiff 78, Florence, Italy, March, 1978), pp. 245-256.
  • [2] -, A class of nonlinear ordinary differential equations with a "characteristic equation", Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 787-790. MR 518979 (80c:34034)
  • [3] R. Conti, Sistemi differenziali ordinari con condizioni lineari, Ann. Mat. Pura. Appl. 46 (1958), 109-130. MR 0105525 (21:4265)
  • [4] W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer-Verlag, Berlin and New York, 1971. MR 0460785 (57:778)
  • [5] C. Corduneanu, Sur les systèmes différentiels de la forme $ y' = A(x,y)y + b(x,y)$, An. Şti. Univ. "Al. I. Cuza" Iaşi Secţ. I. Mat. (N.S.) 4 (1958), 45-52. MR 0103306 (21:2081)
  • [6] P. Hartman, Disconjugacy and Wronskians, Japan-U.S. Seminar on Ordinary Differential Equations and Functional Equations (M. Urabe, Ed.), Lecture Notes in Math., vol. 243, Springer-Verlag, Berlin and New York, 1971, pp. 208-218. MR 0402178 (53:5999)
  • [7] -, Ordinary differential equations, Wiley, New York, 1964. MR 0171038 (30:1270)
  • [8] L. K. Jackson, Existence and uniqueness of solutions of boundary value problems for third order differential equations, J. Differential Equations 13 (1973), 432-437. MR 0335925 (49:703)
  • [9] -, Subfunctions and second order differential inequalities, Advances in Math. 2 (1968), 307-363. MR 0229896 (37:5462)
  • [10] -, Disconjugacy conditions for linear third order differential equations, J. Differential Equations 4 (1968), 369-372. MR 0226112 (37:1702)
  • [11] L. Jackson and K. Schrader, Subfunctions and third order differential inequalities, J. Differential Equations 8 (1970), 180-194. MR 0257525 (41:2175)
  • [12] -, Existence and uniqueness of solutions of boundary value problems for third order differential equations, J. Differential Equations 9 (1971), 46-54. MR 0269920 (42:4813)
  • [13] A. G. Kartsatos, Nonzero solutions to boundary value problems for nonlinear systems, Pacific J. Math. 5 (1974), 425-433. MR 0377164 (51:13337)
  • [14] -, Bounded solutions to perturbed nonlinear systems and asymptotic relationships, J. Reine Angew. Math. 273 (1975), 170-177. MR 0372348 (51:8564)
  • [15] A. Ju. Levin, Nonoscillation of solutions of the equation $ {x^{(n)}} + {p_1}(t){x^{(n - 1)}} + \cdots + {p_n}(t)x = 0$, Russian Math. Surveys 24 (1969), 43-49. MR 0254328 (40:7537)
  • [16] K. W. Schrader, Differential inequalities for second and third order equations, J. Differential Equations 25 (1977), 203-215. MR 0457828 (56:16032)
  • [17] -, A note on second order differential inequalities, Proc. Amer. Math. Soc. 19 (1968), 1007-1012. MR 0234097 (38:2416)
  • [18] J. D. Schuur, A class of nonlinear ordinary differential equations which inherit linear-like asymptotic behavior, Nonlinear Analysis, T.M.A. 3 (1979), 81-86. MR 520475 (80b:34037)
  • [19] C. A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York, 1968. MR 0463570 (57:3515)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C11, 34A40

Retrieve articles in all journals with MSC: 34C11, 34A40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0619988-7
Keywords: Differential inequalities, subfunctions, disconjugacy, asymptotic behaviour
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society