A state-dependent Chandrasekhar integral equation

[1] J. Banas, On the superposition operator and integrable solutions of some functional equations, Nonlinear Anal. 12 (1988), 777–784.

[2] J. Banas and Z. Knap, Integrable solutions of a functional integral equation, Rev. Mate. Univer. Comp. Madrid 2 (1989), no. 1, 1–8.

[3] A. Buica, Existence and continuous dependence of solutions of some functional-differential equations, Publication of the Seminar on Fixed Point Theory, Cluj-Napoca, 3 (1995), 1–14.

[4] Gh. Coman, G. Pavel, I. Rus and I.A. Rus, Introducere in teoria ecuatilllor, Editura Decia, Cluj-Napoca, 1976.

[5] J. Bana´s, M. Lecko and W.G. El-Sayed, Existence theorems for some quadratic integral equations, J. Math. Anal. Appl. 222 (1998), 276–285.

[6] J. Caballero, A.B. Mingrarelli and K. Sadarangani, Existence of solution of an integral equation of Chandrasekhar type in the radiative transfer, Electron. J. Differ. Equ. 27 (2006), 1—11.

[7] S. Chandrasekhar, Radiative Transfer, Oxford University Press, New York, 1960.

[8] S. Chandrasekhar, On the radiative equilibrium of a stellar atmosphere XIV, Astrophys. J. 105 (1947), 164–203.

[9] R.F. Curtain and A.J. Pritchard, Functional analysis in modern applied mathematics, Academic Press, 1977.

[10] E. Eder, The functional-differential equation x’(t)=x(x(t)), J. Differential Equ., 54 (1984), no. 3, 390–400.

[11] M. Feˇckan, On a certain type of functional-differential equations, Math. Slovaca, 43 (1993), no. 1, 39–43.

[12] A.M.A. El-Sayed, E.A.A. Ziada and H.H.G. Hashem, Numerical solution of an integral equation of Chandrasekhar type in the theory of radiative transfer, Int. J. Adv. Sci. Engin. Technol. 5 (2017), no. 4, 1–5.

[13] A.M.A. El-Sayed and R.G. Ahmed, Solvability of the functional integro-differential equation with self-reference and state-dependence, J. Nonl. Sci. Appl. 13 (2020), 1–8.

[14] A.M.A. El-Sayed, H. El-Owaidy and R.G. Ahmed, Solvability of a boundary value problem of self-reference functional differential equation with infinite point and integral conditions, J. Math. Computer Sci. 21 (2020), 296-–308.

[15] A.M.A. El-Sayed and H.R. Ebead, On the solvability of a self-reference functional and quadratic functional integral equations, Filomat 34 (2020), no. 1, 1-–14.

[16] A.M.A. El-Sayed, E.M Hamdallah and H.R. Ebead, Positive nondecreasing solutions of a self-reference differential equation with two state-delay functions, Adv. Math. Sci. J. 9 (2020), no. 12, 10357—10365.

[17] A.M.A. El-Sayed, E.M. Hamdallah and H.R. Ebead, On a nonlocal boundary value problem of a state-dependent differential equation, Math. 9 (2021), no. 21, 2800.

[18] A.M.A. El-Sayed and H.R. Ebead, Existence of positive solutions for a state-dependent hybrid functional differential equation, IAENG Int. J. Appl. Math. 50 (2020), no. 4, 883–889.

[19] A.M.A. El-Sayed and H.H.G. Hashem, A state-dependent integral equation of fractional order, Adv. Math. Sci. J. 10 (2021), no. 2, 811-–817.

[20] A.M.A. El-Sayed and Y.M.Y. Omar, p-Chandrasekhar integral equation, Adv. Math. Sci. J. 9 (2020), no. 12, 10305—10311.

[21] F. Haqa, K. Shahb, G. UR-Rahmanc and M. Shahzad, Existence results for a coupled systems of Chandrasekhar quadratic integral equations, Commun. Nonlinear Anal. 3 (2017), 15—22.

[22] M.A. Hernandez-Veron, E. Mart´ınez and S. Singh, On the Chandrasekhar integral equation, Comput. Math. Meth. 3 (2021), no. 6, e1150.

[23] H.H.G. Hashem, Continuous dependence of solutions of coupled systems of state-dependent functional equations, Adv. Differ. Equ. Control Process. 22 (2020), no. 2, 121–135.

[24] F. Hartung, T.Krisztin, H. Walther and J. Wu, Functional differential equations with state-dependent delays: Theory and applications, Handbook of Differential Equations: Ordinary Differential Equations 3 (2006), 435–545.

[25] RJ. Oberg, On the local existence of solution of certain functional-differential equations, Proc. Amer. Math. Soc. 20 (1960), 295–302.

[26] N.T.T. Lan and P. Eduardo, A two-point boundary value problem for a differential equation with self-reference, Electron. J. Math. Anal. Appl. 6 (2018), no. 1, 25–30.

[27] M. Miranda and E. Pascali, On a type of evolution of self-referred and hereditary phenomena, Aequationes Math. 71 (2006), 253-–268.

[28] E. Pascali, Existence of solutions to a self-referred and hereditary system of differential equations, Electron. J. Diff. Eqns. 7 (2006), 1–7.

[29] Y.-W. Lin and T.-T. Lu, Qualitative behavior of a state-dependent functional differential equation, J. Appl. Comput. Math. 2 (2013), no. 5, 2–5.

[30] M.Y. Waziri, W.J. Leong, M. Abu Hassan and M. Monsi, A low memory solver for integral equations of Chandrasekhar type in the Radiative transfer problems, Math. Prob. Engin. 2011 (2011), Article ID 467017, 12 pages. doi:10.1155/2011/467017