Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T13:09:24.615Z Has data issue: false hasContentIssue false

Uniqueness of solutions for a class of non-linear Volterra integral equations with convolution kernel

Published online by Cambridge University Press:  24 October 2008

P. J. Bushell
Affiliation:
Mathematics Division, University of Sussex
W. Okrasinski
Affiliation:
Institute of Mathematics, University of Wroclaw, Poland

Extract

The non-linear Volterra integral equation

has been studied recently in connection with non-linear diffusion and percolation problems [4, 6, 10]. The existence, uniqueness and qualitative behaviour of non-negative, non-trivial solutions are the questions of physical interest.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Askhabov, S. N.Karapetyants, N. K. and Yakubov, A. Ya.. A nonlinear equation of convolution type (in Russian). Differentsial'nye Uravneniya 22 (1986), 16061609.Google Scholar
[2]Bushell, P. J.On a class of Volterra and Fredholm nonlinear integral equations. Math. Proc. Cambridge Philos. Soc. 79 (1976), 329335.CrossRefGoogle Scholar
[3]Bushell, P. J.The Cayley–Hilbert metric and positive operators. Linear Algebra Appl. 84 (1986), 271280.Google Scholar
[4]Goncerzewicz, J., Marcinkowska, H., Okrasinski, W. and Tabisz, K.. On the percolation of water from a cylindrical reservoir into the surrounding soil. Zastos. Mat. 16 (1978), 249261.Google Scholar
[5]Gripenberg, G.. Unique solutions of some Volterra integral equations. Math. Scand. 48 (1981), 5967.CrossRefGoogle Scholar
[6]Keller, J. J.Propagation of simple nonlinear waves in gas filled tubes with friction. Z. Angew. Math. Phys. 32 (1981), 170181.CrossRefGoogle Scholar
[7]Krasnoselskii, M. A.Positive Solutions of Operator Equations (Noordhoff, 1964).Google Scholar
[8]Miller, R. K.Nonlinear Volterra Integral Equations (Benjamin, 1971).Google Scholar
[9]Okrasinski, W.. Nonnegative solutions of some nonlinear integral equations. Ann. Polon. Math. 44 (1984), 209218.Google Scholar
[10]Schneider, W. R.The general solution of a nonlinear integral equation of convolution type. Z. Angew. Math. Phys. 33 (1982), 140142.Google Scholar
[11]Walter, W.. Differential and Integral Inequalities (Springer-Verlag, 1970).CrossRefGoogle Scholar