THE EXISTENCE OF A SOLUTION FOR SEMI-LINEAR
ABSTRACT DIFFERENTIAL EQUATIONS WITH INFINITE
$B-$CHAINS OF THE CHARACTERISTIC SHEAF

A. Qazza1, R. Hatamleh2
1Department of Mathematics
Zarqa University
P.O. Box 132222, Zarqa, 13132, JORDAN
2Department of Mathematics
Jadara University
P.O. Box 733, Irbid, 21110, JORDAN

Abstract

Initial-value problems for a semi-linear differential operator equations with singular linear part are considered. The existence of the infinite $B-$chains for the characteristic sheaf $\lambda A+B$ is assumed. In this case conditions for solvability have been obtained. The results are applied to a mixed problem for a partial differential equation.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 5
Year: 2018

DOI: 10.12732/ijam.v31i5.7

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References

  1. [1] R.W. Carroll, E. Showalter, Singular and Degenerate Cauchy Problems, Academic Press, New York - London (1976).
  2. [2] J. Dieudonne, Foundations of Modern Analysis, Academic Press, New York-London (1960).
  3. [3] A. Favini, P. Plazzi, Some results concerning the abstract nonlinear equation DtMu(t)+Lu(t) = f(t,Ku(t)), Circuits Systems and Signal Processing, 5, No 2 (1986), 261-274.
  4. [4] A. Favini, A. Rutkas, Existence and uniqueness of solutions of some abstract degenerate nonlinear equations, Differential Integral Equations, 12, No 3 (1999), 373-394.
  5. [5] P.S. Kabalyants, A.G. Rutkas, Two theorems on existence of solutions of a quasilinear singular differential-operator equation, Nonlinear Oscillations, 3, No 3 (2000), 358-365.
  6. [6] M.M. Vainberg, V.A. Trenogin, Branching Theory of Solutions of Nonlinear Equations, Moscow, Nauka Publ. (1969) (in Russian).