Sentence examples for bounded solution of a from inspiring English sources
Now, we study the existence and uniqueness of the bounded solution of a functional equation using again Corollary 2.2.
As a consequence of the presented results, we discuss the existence and uniqueness of the common bounded solution of a functional equation arising in dynamic programming.
Like ({H_infty }) filter design without delay, the filtering problem is transformed to seeking a bounded solution of a Riccati differential equation.
The presented results are applied to obtain the solution of an integral equation and the bounded solution of a functional equation arising in dynamic programming.
Also Cuevas and Pinto [4] have shown that under certain conditions there is a one to one correspondence between weighted bounded solutions of a linear Volterra difference equation with unbounded delay and its perturbation.
Now, we investigate bounded functions satisfying each of (2.2) and (2.3) (see [4, 11 13] for bounded solutions of an exponential functional equation).
For example, Medvedev [9] gave a sufficient condition to guarantee the existence of a bounded solution of the following equation: x ′ = A ( t, x ) + f ( t ), (1.1).
Recently Song [4] obtained a more general result than that of Theorem 3.2, that is, under the assumption of asymptotic almost periodicity of a bounded solution of (2.7), he showed the existence of an almost periodic solution of the limiting equation (2.12) of (2.7).
If the bounded solution of (1.1) is an a.a.p. sequence, then the system (1.1) has an a.p. solution.
As a consequence of Theorem 2 every bounded solution of (1) approaches either an equilibrium solution or a period-two solution and every unbounded solution is asymptotic to the point at infinity in a monotonic way.
