| Subject |
Impulsive and functional differential equations |
| Title |
Solvability of nonlinear boundary value problem |
| Author(s) |
Dulat Dzhumabaev, Elmira Bakirova |
| Keywords |
integro-differential equation, nonlinear boundary value problem, parameterization method, solvability, impulse effect. |
| Abstract |
Abstract: Consider the nonlinear two-point boundary value problem for the Fredholm integro-differential equation with impulse effect
dx/dt=f_0 (t,x)+∫_0^T▒〖f_1 (t,s,x(s))ds〗, t∈(0,T)\{θ}, x∈R^n, (1)
〖 A〗_0 lim┬(t→θ-0)〖x(t)〗+B_0 lim┬(t→θ+0)〖x(t)=d_0 〗, (2)
〖 A〗_1 x(0)+B_1 x(T)=d_1. (3)
In the report based on parametrization method [1, 2] the conditions for solvability of problem (1) – (3) are established. Approximation method for finding its solutions is constructed. The problem of choice of initial approximation to the solution and algorithms for its finding are studied.
Algorithms for finding solution to problem (1) – (3) needs solving the special Cauchy problem for integro-differential equations with parameters.
Sufficient conditions for the existence of unique solution to the special Cauchy problem and the estimate of difference of its solutions are obtained in [3]. The solvability conditions for the linear boundary value problem with parameter for the Fredholm integro-differential equation with impulse effect is given in [4].
|
