g. darbo [rend. sem. math. univ. padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. in this paper, we apply the darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.

in this paper, the optimal boundary control problem for distributed parabolic systems, involving second orderoperator with an infinite number of variables, in which constant lags appear in the integral form both in the state equations and in the boundary condition is considered. some specific properties of the optimal control arediscussed.

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...