Global existence and estimates of the solutions to nonlinear integral equations

  • Authors

    • Alexander G. Ramm Mathematics Department, Kansas State University, CW 207, Manhattan, KS 66506-2602, USA
    2017-03-14
    https://doi.org/10.14419/gjma.v5i1.7306
  • Nonlinear Integral Equations

  • 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. [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.

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  • 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