EXISTENCE OF SOLUTIONS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Authors

  • K. BALACHANDRAN Department of Mathematics, Bharathiar University, Coimbatore -641 046, INDIA.
  • S. MARSHAL ANTHONI Department of Mathematics, Bharathiar University, Coimbatore -641 046, INDIA.

DOI:

https://doi.org/10.5556/j.tkjm.30.1999.4236

Keywords:

Neutral functional differential equation, Cosine operators, Schaefer theorem

Abstract

Sufficient conditions for existence of mild solutions for second order neutral functional differential equations are established by using the theory of strongly continuous cosine families and the Schaefer theorem.

References

J. Ball, Initial boundary value problems for an extensible beam, Journal of Mathematical Analysis and Applications 42(1973), 61-90.

J. Bochenek, An abstract nonlinear second order differential equation, Annales Polonici Mathematici 54(1991), 155-166.

W. E. Fitzgibbon, Global existence and boundedness of solutions to the extensible beam equation, SIAM Journal of Mathematical Analysis 13(1982), 739-745.

E. Hernandez and H. R. Henriquez, Existence results for partial neutral functional integrod­ifferential equations with unbounded delay, Journal of mathematical Analysis and Applica­tions 221(1998), 452-475.

S. K. Ntouyas, Global existence for neutral functional integrodifferential equations, Nonlinear Analysis: Theory, Methods and Applications 30(1997), 2133-2142

S. K. Ntouyas and P. Ch. Tsamatos, Global existence for second order semilinear ordi­nary and delay integrodifferential equations with nonlocal conditons, Applicable Analysis, 67(1997), 245-257.

H. Schaefer, Uber 如 methode der a priori schranken, Mathematische Annalem 129(1955), 415-416.

C. C. Travis and G. F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Mathematica Academiae Scientiarum Hungaricae 32(1978), 75-96.

C. C. Travis and G. F. Webb, Compactness, regularity and uniform continuity properties of strongly continuous cosine families, Houston Journal of Mathematics 3(1977), 555-567

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Published

1999-12-01

How to Cite

BALACHANDRAN, K., & ANTHONI, S. M. (1999). EXISTENCE OF SOLUTIONS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS. Tamkang Journal of Mathematics, 30(4), 299-309. https://doi.org/10.5556/j.tkjm.30.1999.4236

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Papers