Positive solutions of singular integral equations - A survey

Dynamic Systems and Applications

Volumn 14, Issue 1, 2005, Pages 1-38

  Agarwal, Ravi P ^a   Meehan, Maria ^b   O'Regan, Donal ^c  

^a Florida Institute of Technology   (United States)

^b UNIVERSITY COLLEGE DUBLIN   (Ireland)

^c NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

Fixed point theorem; Fredholm equation; Positive solution; Singular; Volterra equation

Indexed keywords

BOUNDARY VALUE PROBLEMS; FUNCTIONS; MATHEMATICAL MODELS; SET THEORY; THEOREM PROVING;

FIXED; FREDHLOM EQUATION; NONLINEAR FUNCTIONS; POINT THEOREM; POSITIVE SOLUTION; SINGULAR; VOLTERRA EQUATION;

INTEGRAL EQUATIONS;

EID: 18344390432     PISSN: 10562176     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. p and continuous solutions for Fredholm integral inclusions, SIM AA, 4(2002). 1-9.
2. R.P. Agarwal, M. Meehan and D. O'Regan, Nonlinear Integral Equations and Inclusions, Nova Science. Publ, New York. 2001.
3. R.P. Agarwal and D.O'Regan, A note on a singular integral equation arising in a problem in communications, Zeitschrift für Angewandte Mathematik und Mechanik. 81(2001), 499-504.
4. R.P. Agarwal and D.O'Regan, Singular Volterra integral equations, Applied Math. Letters, 13 (1) (2000), 115-120.
5. R.P. Agarwal and D. O'Regan, The solution set of integral inclusions on the half line, Integral and Integrodifferential Equations: Theory, Methods and Applications (edited by R.P. Agarwal and D. O'Regan), Gordon and Breach Publishers, 2000, 1-7.
6. R.P. Agarwal and D. O'Regan, Singular integral equations arising in Homann flow, Dynamics of Continuous, Discrete and Impulsive Systems (Ser B: Applications and Algorithms), to appear.
7. R.P. Agarwal and D. O'Regan, Volterra integral equations: the singular case, Hokkaido Math. Journal, to appear.
8. R.P. Agarwal, D.O'Regan and P.J.Y. Wong, Positive solutions of differential, difference and integral equations, Kluwer Academic Publishers, Dordrecht, 1999.
9. P.J. Bushell, On a class of Volterra and Fredholm nonlinear integral equations, Math. Proc. Camb. Phil. Soc., 79(1976), 329-335.
10. P.J. Bushell and W. Okrasinski, Nonlinear Volterra integral equations with convolution kernel, J. London Math. Soc., 41(1990), no.2, 503-510.
11. P.J. Bushell and W. Okrasinski, Uniqueness of solutions for a class of nonlinear Volterra integral equations with convolution kernel, Math. Proc. Camb. Phil. Soc., 106(1989), 547-552.
12. C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, New York, 1990.
13. C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, 1973.
14. C. Corduneanu, Admissibility with respect to an integral operator and applications, SIAM Studies Appl. Math., 5(1969), 55-63.
15. L.H. Erbe, S. Hu and H. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl., 184(1994), 640-648.
16. L.H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc., 120(1994), 743-748.
17. G. Gripenberg, On the uniqueness of solutions of Volterra equations, J. Integral Equations Appl., 2(1990), no.3, 421-430.
18. G. Gripenberg, Unique solutions of some Volterra integral equations, Math. Scand., 48(1981), 59-67.
19. G. Gripenberg, S.O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia of Mathematics and its Applications 34, Camb. Univ. Press, New York, 1990.
20. M.A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Macmillan Co., New York, 1964.
21. M.A. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff Ltd., Groningen, 1964.
22. J.W. Lee and D. O'Regan, Existence principles for nonlinear equations on semi-infinite and half-open intervals, Advances in Nonlinear Dynamics (edited by S.V. Sivasundarem and A.A. Martynuk), Gordon and Breach Science Publ. Ltd., Amsterdam, 1997, 355-364.
23. W. Lian, F. Wong and C. Yeh, On the existence of positive solutions of nonlinear second order differential equations, Proc. Amer. Math. Soc., 124(1996), 1117-1126.
24. M. Meehan and D. O'Regan, Positive solutions of Volterra integral equations using integral inequalities, J. Inequal. Appl., 7(2002), no. 2, 285-307.
25. p solutions of Hammerstein integral equations, Arch. Math., 76(2001), no. 5, 366-376.
26. M. Meehan and D. O'Regan, A note on positive solutions of Fredholm integral equations and related boundary value problems, Math. Proc. R. Ir. Acad., 101A(2001), no. 1, 75-85.
27. M. Meehan and D. O'Regan, Positive solutions of singular integral equations, J. Integral Equationn Appl., 12(2000), no. 3, 271-280.
28. M. Meehan and D. O'Regan, Multiple nonnegative solutions of nonlinear integral equations on compact and semi-infinite intervals, Appl. Anal., 74(2000), no.3-4, 413-427.
29. M. Meehan and D. O'Regan, Positive solutions of singular and nonsingular Fredholm integral equations, J. Math. Anal. Appl., 240(1999), no. 2, 416-432.
30. M. Meehan and D. O'Regan, Existence theory for nonlinear Fredholm and Volterra integral equations on half open intervals, Nonlinear Anal., 35(1999), no.3, Ser. A: Theory, Methods, 355-387.
31. M. Meehan and D. O'Regan, Existence theory for nonlinear Volterra integrodifferential and integral equations, Nonlinear Anal., Theory, Methods and Appl., 31(1998), no.3-4, 317-341.
32. D. O'Regan, Existence theory for nonlinear Volterra and Hammerstein integral equations, Dynamical Systems and Appl., (edited by R.P. Agarwal), World Scientific Series in Applicable Analysis, River Edge, New Jersey, Vol.4, (1995), 601-615.
33. D. O'Regau, Theory of Singular Boundary Value Problems, World Scientific Press, Singapore, 1994.
34. D. O'Regan and M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, Kluwer Acad. Publ., Dordrecht, 1998.
35. C.A. Stuart, Positive solutions of a nonlinear integral equation, Math. Ann., 192(19 71), 119-124.
36. L. Von Wolfersdorf, Travelling wave solutions of a nonlinear diffusion equation with integral term, Z. Anal. Anwendungen, 9(1990), 303-312.
37. J. Wang, W. Gao and Z. Zhang, Singular nonlinear boundary value problems arising in boundary layer theory, Jour. Math. Anal. Appl., 233(1999), 246-256.
38. Dong Wei, Uniqueness of solutions for a class of nonlinear Volterra integral equations without continuity, Appl. Math. Mech. (English Ed.), 18(1997), no.12, 1191-1196.
39. P.P. Zabreyko, A.I. Koshelev, M.A. Krasnoselskii, S.G. Milkin, L.S. Rakoshchik and V.Y. Stetsenko, Integral Equations-a Reference Text, Noordhoff International Publ., Leyden, 1975.