Abstract:
We prove a theorem on the unique existence of a solution to a nonlinear equation with maxima and demonstrate its continuous dependence on the initial function and the parameter of the problem. We also establish conditions for the existence of a nonzero solution to a two-point boundary-value periodic problem in dependence of both linear and nonlinear terms of the equation.
Keywords:initial function, parameter, compact, equation with maxima, theorem on the unique existence of a solution, two-point boundary-value periodic problem, fundamental matrix, operator, fixed point, admissible vector of a matrix.