Sentence examples for maximal solution for from inspiring English sources

Our main existence theorem for a maximal solution for FHDE (2.1) is as follows.

Let be the maximal solution for the impulsive Cauchy problem (2.4).

Our main existence theorem for maximal solution for BVPHDEF (1) is the following.

In [4] we proved that if g is a c-Lipschitz functional field, then problem (2.3) has a unique maximal solution for any η ∈ M ˜.

In the previous section, we have proved that there exist coupled minimal and maximal solutions for the differential equation equation (15).

Difference from the above mentioned work is that in this paper we introduce new type growth condition of nonlinearity which covers a large number of nonlinear functions; at the same time, the existence, estimation of the lower and upper bounds and the convergent iterative scheme of minimal and maximal solutions for system (1.1) are also established.

In the rest of the paper, the solution of (1.1) always means the maximal solution of (1.1), for which the comparison principle is valid.

Let be a solution of (1.2) in, then is said to be a maximal solution of (1.2), if for every solution of (1.2) existing on, the inequality,, holds.

Then (r(t)) is said to be a maximal solution of (2.2) if, for every solution (u(t)) of (2.2) existing on ((0, +infty)), the inequality (u(t)leq r(t)), (tin 0, +infty)) holds.

Let (g:(0,+infty timesmathbb{R}rightarrowmathbb{R}) (t,u rightarrow g t,u) be continuous and satisfy inequality (2.3), and let η be the maximal solution of (2.2) existing for (tin 0,+infty)).

This transformation ensures that the new method for computing the maximal solution of the nonlinear matrix equation converges quadratically.