Solvability of a Quadratic Integral Equation of Fredholm Type Via a Modified Argument

Abstract (pdf)

Full text (pdf)

1. R.P. Agarwal, J. Banaś, K. Banaś, D. O'Regan, Solvability of a quadratic Hammerstein integral equation in the class of functions having limits at infinity, J. Int. Eq. Appl. 23 (2011) 157-181.
2. R.P. Agarwal, D. O'Regan, Infinite Interval Problems for Differential, Difference and Integral equations, Kluwer Academic Publishers, Dordrecht, 2001.
3. R.P. Agarwal, D. O'Regan, P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 1999.
4. C. Bacoṯiu, Volterra-Fredholm nonlinear systems with modified argument via weakly Picard operators theory, Carpath. J. Math. 24 (2) (2008) 1-19.
5. J. Banaś, J. Caballero, J. Rocha, K. Sadarangani, Monotonic solutions of a class of quadratic integral equations of Volterra type, Comput. Math. Appl. 49 (2005) 943-952.
6. J. Banaś, M. Lecko, W.G. El-Sayed, Existence theorems of some quadratic integral equation, J. Math. Anal. Appl. 222 (1998) 276-285.
7. J. Banaś, R. Nalepa, On the space of functions with growths tempered by a modulus of continuity and its applications, J. Func. Spac. Appl. (2013), Article ID 820437, 13 pp.
8. M. Benchohra, M.A. Darwish, On unique solvability of quadratic integral equations with linear modification of the argument, Miskolc Math. Notes 10 (1) (2009) 3-10.
9. J. Caballero, M.A. Darwish, K. Sadarangani, Solvability of a quadratic integral equation of Fredholm type in Hölder spaces, Electron. J. Differential Equations 31 (2014) 1-10.
10. J. Caballero, B. Lopez, K. Sadarangani, Existence of nondecreasing and continuous solutions of an integral equation with linear modification of the argument, Acta Math.Sin. (English Series) 23 (2003) 1719-1728.
11. J. Caballero, J. Rocha, K. Sadarangani, On monotonic solutions of an integral equation of Volterra type, J. Comput. Appl. Math. 174 (2005) 119-133.
12. K.M. Case, P.F. Zweifel, Linear Transport Theory, Addison Wesley, Reading, M. A 1967.
13. S. Chandrasekhar, Radiative transfer, Dover Publications, New York, 1960.
14. M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119.
15. M.A. Darwish, On solvability of some quadratic functional-integral equation in Banach algebras, Commun. Appl. Anal. 11 (2007) 441-450.
16. M.A. Darwish, S.K. Ntouyas, On a quadratic fractional Hammerstein-Volterra integral equations with linear modification of the argument, Nonlinear Anal. 74 (2011) 3510-3517.
17. M. Dobriṯoiu, Analysis of a nonlinear integral equation with modified argument from physics, Int. J. Math. Models and Meth. Appl. Sci. 3 (2) (2008) 403-412.
18. S. Hu, M. Khavani, W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal. 34 (1989) 261-266.
19. T. Kato, J.B. Mcleod, The functional-differential equation y’(x) = ay(λx) + by(x), Bull. Amer. Math. Soc. 77 (1971) 891-937.
20. C.T. Kelly, Approximation of solutions of some quadratic integral equations in transport theory, J. Int. Eq. 4 (1982) 221-237.
21. M. Lauran, Existence results for some differential equations with deviating argument, Filomat 25 (2) (2011) 21-31.
22. V. Mureşan, A functional-integral equation with linear modification of the argument, via weakly Picard operators, Fixed Point Theory 9 (1) (2008) 189-197.
23. V. Mureşan, A Fredholm-Volterra integro-differential equation with linear modification of the argument, J. Appl. Math. 3 (2) (2010) 147-158.
24. J.M.A. Toledano, T.D. Benavides, G. L Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhäuser Verlag, 1997.