Global existence and estimates of the solutions to nonlinear integral equations
DOI:
https://doi.org/10.14419/gjma.v5i1.7306Keywords:
Nonlinear Integral EquationsAbstract
It is proved that a class of nonlinear integral equations of the Volterra-Hammerstein type has a global solution, that is, solutions defined for all \(t\ge 0\), and estimates of these solutions as \(t\to \infty\) are obtained. The argument uses a nonlinear differential inequality which was proved by the author and has broad
applications.
References
- [1] K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985.
[2] A.G.Ramm, Asymptotic stability of solutions to abstract differential equations, Journ. of Abstract Diff. Equations and Applications (JADEA), 1, N1, (2010), 27-34.
[3] A.G.Ramm, A nonlinear inequality and evolution problems, Journ, Ineq. and Special Funct., (JIASF), 1, N1, (2010), 1-9.
[4] A.G.Ramm, Stability of solutions to some evolution problems, Chaotic Modeling and Simulation (CMSIM), 1, (2011), 17-27.
[5] A.G.Ramm, Large-time behavior of solutions to evolution equations, in Handbook of Applications of Chaos Theory, Chapman and Hall/CRC, (ed. C.Skiadas), pp. 183-200.
[6] P. Zabreiko et al, Integral equations: a reference text, Leyden, Noordhoff International Pub., 1975.
Downloads
How to Cite
Ramm, A. G. (2017). Global existence and estimates of the solutions to nonlinear integral equations. Global Journal of Mathematical Analysis, 5(1), 19-20. https://doi.org/10.14419/gjma.v5i1.7306
Received date: January 30, 2017
Accepted date: March 1, 2017
Published date: March 14, 2017