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Topological transversality: applications to differential equations

Published online by Cambridge University Press:  17 April 2009

T. Sengadir  and
A.K. Pani
T. Sengadir
Affiliation:
Institute of Mathematical SciencesCIT Campus Madras 600113India
A.K. Pani
Affiliation:
Department of MathematicsIndian Institute of TechnologyPowai Bombay 400 076India
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Abstract

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In this paper, existence results for both integro-differential and functional differential equations are discussed using topological transversality arguments. As applications, third and fourth order boundary value problems are considered. For third order problems, an example has been cited to show that our results cover a wider class of problems than Theorem 2.3 of D.J. O'Regan, Topological transversality: Applications to third order boundary value problems, SIAM J. Math. Anal. 18 (1987) 630–641.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 2 , October 1994 , pp. 251 - 264
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Aftabizadeh, A.R. and Leela, S.R., ‘Existence results for boundary value problems of integro-differential equations’, in Differential Equations: Qualitative Theory 47 (North Holland, Szeged, 1984), pp. 23–35.Google Scholar
[2]Agarwal, R.P., ‘Boundary value problems for higher order integro-differential equations’, Nonlinear Analysis. TMA 7 (1983), 259–240.CrossRefGoogle Scholar
[3]Erbe, L.H. and Krawcewicz, W., ‘Boundary value problems for differential inclusions’, in Differential Equations: Stability and Control 127 (Marcel Dekker, 1990), pp. 115–135.Google Scholar
[4]Granas, A., ‘Sur la methode de continuite de Poincare’, C.R. Acad. Sci. Paris 282 (1976), 983–985.Google Scholar
[5]Granas, A., Guenther, R.B. and Lee, J.W., ‘On a theorem of S. Bernstein’, Pacific J. Math. 74 (1978), 67–82.CrossRefGoogle Scholar
[6]Hu, S. and Lakshmikantham, V., ‘Periodic boundary value problems for second order integro-differential equations of Volterra type’, Applicable Analysis 21 (1986), 199–205.CrossRefGoogle Scholar
[7]Lee, J.W. and O'Regan, D., ‘Existence results for differential delay equations II’, Nonlinear Analysis TMA 17 (1991), 683–702.CrossRefGoogle Scholar
[8]Ntouyas, S.K. and Tsamatos, P.Ch., ‘Existence of solutions of boundary value problems for functional differential equations’, Int. J. Math. and Math. Sci. 14 (1991), 509–516.CrossRefGoogle Scholar
[9]Ntouyas, S.K. and Tsamathos, P.Ch., ‘Existence of solutions of boundary value problems and deviating arguments via the topological transversality method’, Proc. Roy. Soc. Edin. 118A (1991), 79–89.Google Scholar
[10]O'Regan, D.J., ‘Topological transversality: Applications to third order boundary value problems’, SIAM J. Math. Anal. 18 (1987), 630–641.CrossRefGoogle Scholar