References

ON THE INTEGRABLE SOLUTIONS OF PRODUCT INTEGRO DIFFERENTIAL EQUATIONS IN DIRECT SUM SPACES


[1] J. S. W. Wong, Square integrable solutions of perturbed linear differential equations, Proc. Royal Soc. of Edinburgh 73A (1974/75), 251-254.

[2] A. Zettl, Square integrable solutions of Proc. Amer. Math. Soc. 26 (1970), 635-639.

[3] A. Zettl, Perturbation of the limit circle case, Quart. J. Math. Oxford 26(3) (1975); 355(3) (1975), 355-360.

[4] S. E. Ibrahim, Boundedness for solutions of general ordinary quasi-differential equations, Journal of the Egyptian Mathematical Society 2 (1994), 33-44.

[5] W. N. Everitt, The number of integrable-square solutions of products of differential expressions, Proc. of the Royal Soc. of Edinburgh 76A (1977), 215-226.

[6] S. E. Ibrahim, On derivatives for solutions of perturbed general quasi-differential equations, Czech. Math. J. 49(124) (1999), Praha 877-890.

[7] S. E. Ibrahim, On the boundedness of solutions for products of quasi-integro differential equations, IJMMS 10(16) (2003), 639-659.

[8] E. H. Yang, On asymptotic behaviour of certain second order integro-differential equations, Proc. Amer. Math. Soc. 90 (1984), 271-276.

[9] A. Zettl, The limit point and limit circle cases for polynomials in differential expressions, Proc. Royal Soc. of Edinburgh 72A (1975), 219-224.

[10] A. Zettl, Formally self-adjoint quasi-differential operators, Rocky Mountain Journal of Mathematics 5 (1975), 453-474.

[11] W. N. Everitt and D. Race, Some remarks on linear ordinary quasi-differential expressions, Proc. London Math. Soc. 54(3) (1987), 300-320.

[12] S. E. Ibrahim, On the boundary conditions for products of general quasi-differential operators in direct sum spaces, IJAM 22(1) (2009), 55-87.

[13] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Oxford University Press, 1987.

[14] A. Zettl, Deficiency indices of polynomials in symmetric differential expressions, II, Proc. Royal Soc. of Edinburgh 73A(20) (1974/75), 301-306.

[15] S. E. Ibrahim, On the essential spectra of regularly solvable operators in direct sum spaces, Rocky Mountain J. Math. 29(2) (1999), 609-644.

[16] S. E. Ibrahim, On the product of self-adjoint Sturm-Liouville differential operators in direct sum spaces, J. of Informatics and Mathematical Sciences 1 (2012), 93-109.

[17] R. P. Agarwal, A note on Grace and Lalli’s paper, J. Math. Anal. Appl. 86 (1982), 471-475.

[18] S. R. Grace and B. S. Lalli, Asymptotic behaviour of certain second order integro-differential equations, J. Math. Anal. 76 (1980), 84-90.

[19] E. H. Yang, Asymptotic behaviour of certain second order integro-differential equations, J. Math. Anal. Appl. 106 (1985), 132-139.