Sidorov, N. A.; Trufanov, A. V.; Sidorov, D. N. Generalized solutions of nonlinear integral-functional equations. (English) Zbl 1120.45002 Nonlinear Bound. Value Probl. 16, 96-106 (2006). Summary: A method of construction of generalized solutions with a point carrier in the singular part is proposed for nonlinear Volterra integral-functional equations \[ \int\limits_0^t K(t,s)(x(s)+ax(\alpha s)+g(s^lx(s),s))ds = f(t) \] with sufficiently smooth kernel and function \(f\); \(\alpha\) and \(a\) are constants, and \(0<|\alpha|<1\). The solution is constructed as a sum of singular and regular components. A special system of linear algebraic equations is used for the construction of the singular component. The regular part is constructed by the method of successive approximations combined with the method of undetermined coefficients. Theorems of existence and uniqueness of the generalized solutions are proved. Cited in 2 Documents MSC: 45G05 Singular nonlinear integral equations 45L05 Theoretical approximation of solutions to integral equations Keywords:Volterra integral equation; distribution; generalized function theory; generalized solutions; nonlinear Volterra integral-functional equations PDFBibTeX XMLCite \textit{N. A. Sidorov} et al., Nonlinear Bound. Value Probl. 16, 96--106 (2006; Zbl 1120.45002)