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Taylor polynomial solutions of nonlinear Volterra–Fredholm integral equations
Applied Mathematics and Computation, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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NONLINEAR VOLTERRA INTEGRAL EQUATIONS WITH CONVOLUTION KERNELS
Bulletin of the London Mathematical Society, 2003Some new results concerning the existence and uniqueness of nontrivial solutions to the title equations are presented.
Mydlarczyk, W., Okrasiński, W.
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APPROXIMATE SOLUTIONS OF NONLINEAR VOLTERRA INTEGRAL EQUATION SYSTEMS
International Journal of Modern Physics B, 2010The purpose of this study is to implement a new approximate method for solving system of nonlinear Volterra integral equations. The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation ...
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Nonlinear Volterra Integral Equations and the Apéry Identities
Bulletin of the London Mathematical Society, 1992The authors study necessary and sufficient conditions for the existence of nontrivial solutions of the Volterra integral equation \(u(x)=\int_ 0^ x k(x-s) g(u(s))ds\). Using the identity \[ \begin{multlined} \int_ a^ x f(s)h(s)ds= \int_ a^ \lambda f(s)\varphi(s)ds+ \int_ a^ \lambda [f(\lambda-f(s)][\varphi(s)-h(s)]ds+\\ +\int_ \lambda^ x [f(s)- f ...
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