Sentence examples for the notion of solution from inspiring English sources

The notion of solution of (2.2) is analogous.

To give a precise meaning of this problem, we introduce the notion of solution of (4.1).

There are some ways to consider the notion of solution for impulsive fractional differential equations; for example, see [29 32].

To continue the solution will need a modification of the notion of solution introduced in Definition 2.1.

Treating the case of general measures needs then greater care, already in specifying the notion of solution one is dealing with.

The main advantage of Caputo' s approach to fractional derivative is that the initial values and the notion of solution parallel the IVP of differential equations, where the derivative is of order one, that is the usual derivative.

To this aim, they extended the notion of solution-tube to systems of first order dynamic inclusions on time scales.

To this aim, we use the following slight modification of the notion of solution-tube introduced in [9].

In particular, a kind of coordinate-wise lower and upper solutions condition was imposed in [4], while Gilbert [5] introduced the notion of solution-tube to systems of first order dynamic equations which generalizes the notions of lower and upper solutions.

Therefore, it turns out that a suitable framework for the well-posedness of the initial-boundary value problem (1.1) is the theory of viscosity solutions (see [4 6]), so we first define the notion of solutions.

We introduce a new variant of the notion of viscosity solution for a class of Hamilton-Jacobi equations, and obtain comparison and existence results for viscosity solutions.