On Solution of Nonlinear Abel-Volterra Integral Equation

Journal of Mathematical Analysis and Applications

Volumn 229, Issue 1, 1999, Pages 41-60

  Kilbas, Anatoly A ^a   Saigo, Megumi ^b  

^a BELARUSIAN STATE UNIVERSITY   (Belarus)

^b FUKUOKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041713874     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6139     Document Type: Article

References (25)

1. Askhabov S. N. Integral equations of convolution type with power nonlinearity. Colloq. Math. 62:1991;49-65.
2. Askhabov S. N., Betilgiriev M. A. Nonlinear convolution type equations. Seminar Analysis. 1990;Karl-Weierstrass-Institute of Mathematics, Berlin. p. 1-30.
3. Askhabov S. N., Betilgiriev M. A. Nonlinear integral equations of convolution type with almost increasing kernels in cones. Differential Equations. 27:1991;234-242.
4. Askhabov S. N., Karapetyants N. K., Yakubov A. Ya. A nonlinear equation of convolution type. Differentsial'nye Uravneniya. 22:1986;1606-1609.
5. Askhabov S. N., Karapetyants N. K., Yakubov A. Ya. Integral equations of convolution type with power nonlinearity and systems of such equations. Soviet Math. Dokl. 41:1990;323-327.
6. Bushell P. J. On a class of Volterra and Fredholm non-linear integral equations. Math. Proc. Cambridge Philos. Soc. 79:1976;329-335.
7. Bushell P. J., Okrasiński W. Nonlinear Volterra integral equations and the Apery identities. Bull. London Math. Soc. 24:1992;478-484.
8. Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. S. Higher Transcendental Functions. 1954;McGraw-Hill, New York.
9. Goncerzewicz J., Marcinkowska H., Okrasiński W., Tabisz K. On the percolation of water from a cylindrical reservoir into the surrounding soil. Zastos. Mat. 16:1978/79;249-261.
10. Gorenflo R., Kilbas A. A. Asymptotic solution of a nonlinear Abel-Volterra integral equation of second kind. J. Fract. Calc. 8:1995;103-117.
11. Gorenflo R., Vessela S. Abel Integral Equations, Analysis and Applications. 1991;Springer-Verlag, Berlin.
12. Gripenberg G. Asymptotic solutions of some nonlinear Volterra integral equations. SIAM J. Math. Anal. 12:1981;595-602.
13. Gripenberg G., Londen S.-O., Staffans O. Volterra Integral and Functional Equations. Encyclopedia of Mathematics and its Applications. 34:1990;Cambridge Univ. Press, Cambridge.
14. Handelsman R. A., Olmstead W. E. Asymptotic solution to a class of nonlinear Volterra integral equations. SIAM J. Appl. Math. 22:1972;373-384.
15. Karapetyants N. K. On a class of nonlinear equations of convolution types. Scientific Proceedings of the Jubilee Seminar on Boundary Value Problems. 1985;Minsk. p. 158-161.
16. Karapetyants N. K., Yakubov A. Ya. A convolution equation with power nonlinearity of negative order. Soviet Math. Dokl. 44:1992;517-520.
17. Keller J. J. Propagation of simple nonlinear waves in gas filled tubes with friction. Z. Angew. Math. Phys. 32:1981;170-181.
18. Kilbas A. A. A nonlinear Volterra integral equation with a weak singularity. Proc. Russian People's Friendship Univ. Math. Ser. 2:1995;47-61.
19. Kilbas A. A., Saigo M. On solution of integral equation of Abel-Volterra type. Differential Integral Equations. 8:1995;993-1011.
20. Okrasiński W. On the existence and uniqueness of nonnegative solutions of a certain nonlinear convolution equation. Ann. Polon. Math. 36:1979;61-72.
21. Okrasiński W. On a nonlinear convolution equation occurring in the theory of water percolation. Ann. Polon. Math. 37:1980;223-229.
22. Okrasiński W. Nonlinear Volterra equations and physical applications. Extracta Math. 4:1989;51-80.
23. Olmstead W. E., Handelsman R. A. Asymptotic solution to a class of nonlinear Volterra integral equation. II. SIAM J. Appl. Math. 30:1976;180-189.
24. Samko S. G., Kilbas A. A., Marichev O. I. Fractional Integrals and Derivatives. Theory and Applications. 1993;Gordon and Breach, New York.
25. Schneider W. R. The general solution of a nonlinear integral equation of convolution type. Z. Angew. Math. Phys. 33:1982;140-142.