Zhuravlyov V. Р.
Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 7-28
We study the problems of existence and representations of the solutions bounded on the entire axis for both linear and nonlinear differential equations with unbounded operator coefficients in the Fr´echet and Banach spaces under the condition of exponential dichotomy on the semiaxes of the corresponding homogeneous equation.
Ukr. Mat. Zh. - 2015. - 67, № 11. - pp. 1477-1490
We consider weakly nonlinear Fredholm integral equations with degenerate kernel in Banach spaces and establish a necessary condition and sufficient conditions for the existence of solutions of equations of this kind. The convergent iterative procedures are proposed for the construction either of a single solution or of at least one possible solution.