Constant-sign solutions for systems of fredholm and volterra integral equations: The singular case

Acta Applicandae Mathematicae

Volumn 103, Issue 3, 2008, Pages 253-276

  Agarwal, Ravi P ^a   O'Regan, Donal ^b   Wong, Patricia J Y ^c  

^a Florida Institute of Technology ^*  (United States)

^b NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^c NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Constant sign solutions; Singular equations; System of Fredholm integral equations; System of Volterra integral equations

Indexed keywords

CONSTANT-SIGN SOLUTIONS; FREDHOLM; FREDHOLM INTEGRAL EQUATIONS; SINGULAR CASE; SINGULAR EQUATIONS; SYSTEM OF FREDHOLM INTEGRAL EQUATIONS; SYSTEM OF VOLTERRA INTEGRAL EQUATIONS; VOLTERRA INTEGRAL EQUATIONS;

INTEGRAL EQUATIONS;

EID: 49549124994     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-008-9234-2     Document Type: Article

References (27)

1. Agarwal, R.P., O'Regan, D.: Singular Volterra integral equations. Appl. Math. Lett. 13, 115-120 (2000)
2. Agarwal, R.P., O'Regan, D.: Singular integral equations arising in Homann flow. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 9, 481-488 (2002)
3. Agarwal, R.P., O'Regan, D.: Volterra integral equations: the singular case. Hokkaido Math. J. 32, 371-381 (2003)
4. Agarwal, R.P., O'Regan, D., Wong, P.J.Y.: Positive Solutions of Differential, Difference and Integral Equations. Kluwer Academic, Dordrecht (1999)
5. Agarwal, R.P., O'Regan, D., Wong, P.J.Y.: Constant-sign solutions of a system of Fredholm integral equations. Acta Appl. Math. 80, 57-94 (2004)
6. Agarwal, R.P., O'Regan, D., Wong, P.J.Y.: Eigenvalues of a system of Fredholm integral equations. Math. Comput. Model. 39, 1113-1150 (2004)
7. Agarwal, R.P., O'Regan, D., Wong, P.J.Y.: Triple solutions of constant sign for a system of Fredholm integral equations. Cubo 6, 1-45 (2004)
8. Agarwal, R.P., O'Regan, D., Wong, P.J.Y.: Constant-sign solutions of a system of integral equations: The semipositone and singular case. Asymptotic Anal. 43, 47-74 (2005)
9. Agarwal, R.P., O'Regan, D., Wong, P.J.Y.: Constant-sign solutions of a system of integral equations with integrable singularities. J. Integr. Equ. Appl. 19, 117-142 (2007)
10. Agarwal, R.P., O'Regan, D., Wong, P.J.Y.: Constant-sign solutions of a system of Volterra integral equations. Comput. Math. Appl. 54, 58-75 (2007)
11. Bonanno, G.: An existence theorem of positive solutions to a singular nonlinear boundary value problem. Comment. Math. Univ. Carol. 36, 609-614 (1995)
12. Bushell, P.J.: On a class of Volterra and Fredholm non-linear integral equations. Math. Proc. Camb. Philos. Soc. 79, 329-335 (1976)
13. Bushell, P.J., Okrasiński, W.: Uniqueness of solutions for a class of nonlinear Volterra integral equations with convolution kernel. Math. Proc. Camb. Philos. Soc. 106, 547-552 (1989)
14. Bushell, P.J., Okrasiński, W.: Nonlinear Volterra integral equations with convolution kernel. J. Lond. Math. Soc. 41, 503-510 (1990)
15. Corduneanu, C.: Integral Equations and Stability of Feedback Systems. Academic Press, San Diego (1973)
16. Corduneanu, C.: Integral Equations and Applications. Cambridge University Press, Cambridge (1990)
17. Dong, W.: Uniqueness of solutions for a class of non-linear Volterra integral equations without continuity. Appl. Math. Mech. 18, 1191-1196 (1997). (English edn.)
18. Gripenberg, G.: Unique solutions of some Volterra integral equations. Math. Scand. 48, 59-67 (1981)
19. Gripenberg, G., Londen, S.-O., Staffans, O.: Volterra Integral and Functional Equations. Encyclopedia of Mathematics and Its Applications, vol. 34. Cambridge University Press, Cambridge (1990)
20. Karlin, S., Nirenberg, L.: On a theorem of P. Nowosad. J. Math. Anal. Appl. 17, 61-67 (1967)
21. Meehan, M., O'Regan, D.: Positive solutions of singular integral equations. J. Integr. Equ. Appl. 12, 271-280 (2000)
22. Meehan, M., O'Regan, D.: A note on singular Volterra functional- differential equations. Math. Proc. R. Ir. Acad. 100A, 73-84 (2000)
23. Meehan, M., O'Regan, D.: Positive solutions of Volterra integral equations using integral inequalities. J. Inequal. Appl. 7, 285-307 (2002)
24. Nowosad, P.: On the integral equation κf = 1/f arising in a problem in communications. J. Math. Anal. Appl. 14, 484-492 (1966)
25. O'Regan, D., Meehan, M.: Existence Theory for Nonlinear Integral and Integrodifferential Equations. Kluwer Academic, Dordrecht (1998)
26. Reynolds, D.W.: On linear singular Volterra integral equations of the second kind. J. Math. Anal. Appl. 103, 230-262 (1984)
27. Wang, J., Gao, W., Zhang, Z.: Singular nonlinear boundary value problems arising in boundary layer theory. J. Math. Anal. Appl. 233, 246-256 (1999)