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On nonoscillatory solutions of differential inclusions
Author(s):
Ravi
P.
Agarwal;
Said
R.
Grace;
Donal
O'Regan
Journal:
Proc. Amer. Math. Soc.
131
(2003),
129-140.
MSC (2000):
Primary 47H10, 34C10
Posted:
June 3, 2002
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Abstract:
This paper introduces a nonoscillatory theory for differential inclusions based on fixed point theory for multivalued maps.
References:
-
- 1.
- R.P. Agarwal, S.R. Grace and D. O'Regan, Oscillation theory for second order dynamic equations, Taylor & Francis, to appear.
- 2.
- C.D. Aliprantis and K.C. Border, Infinite dimensional analysis, Springer Verlag, 1994. MR 96k:46001
- 3.
- J.P. Aubin and A. Cellina, Differential inclusions, Springer, Berlin, 1984. MR 85j:49010
- 4.
- M. Cecchi, M. Marini and P. Zecca, Existence of bounded solutions for multivalued differential systems, Nonlinear Analysis, 9 (1985), 775-786. MR 86j:34012
- 5.
- N. Dunford and J. Schwartz, Linear Operators, Interscience, New York, 1958. Reprint MR 90g:47001a
- 6.
- L.H. Erbe, Q.K. Kong and B.G. Zhang, Oscillation theory for functional differential equations, Marcel Dekker, New York, 1995. MR 96c:34147
- 7.
- P.M. Fitzpatrick and W.V. Petryshyn, Fixed point theorems for multivalued noncompact acyclic mappings, Pacific Jour. Math., 54 (1974), 17-23. MR 53:8973
- 8.
- M. Frigon, Théorèmes d'existence de solutions d'inclusions différentielles, Topological Methods in Differential Equations and Inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C, Vol 472, Kluwer Acad. Publ., Dordrecht, 1995, 51-87. MR 96m:34025
- 9.
- I. Gyori and G. Ladas, Oscillation theory of delay differential equations with applications, Clarendon Press, Oxford, 1991. MR 93m:34109
- 10.
- I.T. Kiguradze, On oscillatory solutions of some ordinary differential equations, Soviet Math. Dokl., 144 (1962), 33-36.
- 11.
- A. Lasota and Z. Opial, An application of the Kututani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 13 (1965), 781-786. MR 33:4370
- 12.
- G.S. Ladde, V. Lakshmikantham and B.G. Zhang, Oscillation theory of differential equations with deviating arguments, Marcel Dekker, New York, 1987. MR 90h:34118
- 13.
- Z. Nehari, A nonlinear oscillation problem, Jour. Differential Eqns., 5 (1969), 452-460. MR 38:3514
- 14.
- D. O'Regan, Integral inclusions of upper semi-continuous or lower semi-continuous type. Proc. Amer. Math. Soc., 124 (1996), 2391-2399. MR 96j:47064
- 15.
- Ch.G. Philos and V.A. Staikos, Oscillation and asymptotic behaviour of second and third order retarded differential equations, Czech. Math. Jour., 32 (1982), 169-182. MR 83g:34082
- 16.
- T. Pruszko, Topological degree methods in multivalued boundary value problems, Nonlinear Analysis, 5 (1981), 953-973. MR 83d:34034
- 17.
- S.M. Rankin, Oscillation of forced second order nonlinear differential equations, Proc. Amer. Math. Society, 59 (1976), 279-282. MR 54:3089
- 18.
- B. Singh, Asymptotic nature of nonoscillatory solutions of
 order retarded differential equations, SIAM Jour. Math. Anal., 6 (1975), 784-795. MR 55:3479 - 19.
- V.A. Staikos and Ch.G. Philos, On the asymptotic behavior of nonoscillatory solutions of differential equations with deviating arguments, Hiroshima Math. Journal, 7 (1977), 9-31. MR 55:8518
- 20.
- R.D. Terry, Some oscillation criteria for delay differential equations of even order, SIAM Jour. Appl. Math., 28 (1975), 319-334. MR 50:13822
- 21.
- J.S.W. Wong, On the second order nonlinear oscillations, Funkcial. Ekvac., 11(1968), 207-234. MR 39:7221
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Additional Information:
Ravi
P.
Agarwal
Affiliation:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Address at time of publication:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901-6975
Email:
agarwal@fit.edu
Said
R.
Grace
Affiliation:
Department of Engineering Mathematics, Cairo University, Orman, Giza 12221, Egypt
Donal
O'Regan
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland
DOI:
10.1090/S0002-9939-02-06492-4
PII:
S 0002-9939(02)06492-4
Keywords:
Differential inclusions,
nonoscillatory,
fixed point theorems
Received by editor(s):
April 4, 2001
Received by editor(s) in revised form:
August 9, 2001
Posted:
June 3, 2002
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2002,
American Mathematical Society
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