A class of linear and nonlinear Fredholm integral equations of the third kind
Keywords:
Fredholm integral equation of the third kind, Linear integral equation, nonlinear integral equation, solution, uniqueness and existence.Abstract
In this paper we are applying a new approach to prove the uniqueness and existence theorems for linear and nonlinear Fredholm integral equations of the third kind.
References
Apartsyn, A.S. 2003. Nonclassical Linear Volterra Equations of the First Kind, VSP, Utrecht.
Asanov, A. 1998. Regularization, Uniqueness and Existence of Solutions of Volterra Equations of the First Kind, VSP, Utrecht.
Bukhgeim, A.L. 1999. Volterra Equations and Inverse Problems, VSP, Utrecht.
Denisov, A.M. 1999. Elements of the Theory of Inverse Problems, VSP, Utrecht.
Imanaliev, M.I. & Asanov, A. 1989. Solutions of systems of Nonlinear Volterra Integral Equations of the First kind, Doklady Akademii Nauk, 309: 1052-1055.
Imanaliev, M.I. & Asanov, A. 2007. Solutions of systems of Volterra Nonlinear Integral Equations of the third kind, Doklady Mathematics, 76: 490-493.
Imanaliev, M.I. & Asanov, A. 2010. Solutions of system of Fredholm linear integral Equations of the third kind, Doklady Mathematics, 81: 115-118.
Imanaliev, M.I., Asanov, A. & Asanov, R.A. 2011. A Class of systems of Linear Fredholm Integral Equations of the third kind, Doklady Mathematics, 83, N2: 227-231.
Lavrent'ev, M.M.1959. The Integral Equations of the first kind, Doklady Akademii Nauk, 127: 31-33.
Lavrent'ev, M.M., Romanov, V.G. & Shishatskii, S.P. 1986. Ill-Posed Problems of Mathematical Physics,Providence, R.I., American Mathematical Society.
Magnitskii, N.A. 1979. Volterra linear integral equations of the first and third kinds, Zhurnal vychislitel'noi matematiki i matematicheskoi fiziki,19:970-989.
Shishatskii, S.P., Asanov, A. & Atamanov, E.R. 2001. Uniqueness Problems for Degenerating Equations and Nonclassical Problems, VSP, Utrecht.