Sentence examples for definition of solutions from inspiring English sources

We give the definition of solutions for the initial value problem (1.1).

We give the definition of solutions to the nonhomogeneous A -harmonic equation and the obstacle problem.

A reasonable formula and definition of solutions for such problem is introduced.

We begin with the definition of solutions to the weighted functional fractional differential equations.

We propose a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal) operators associated with regular Dirichlet forms and with measure data.

where 0 < α ≤ 1, D α is the Riemann-Liouville fractional derivative, y ˜ ( t ) = t 1 − α y ( t ), f : ( 0, b ] × B → R is a given function satisfying some assumptions, and ℬ is the phase space that will be specified later. We give the definition of solutions and investigate the existence and continuous dependence of solutions to such equations in the space C 1 − α ( ( a, b ] ).

Firstly, we present the definition of solution to SVIE (1.1).

Firstly, we give the definition of solution to (1.2).

Nevertheless, the definition of solution element (SE) is modified from that of Chang.

In Section 3, we present the definition of solution for (1.1 - 1.3 1.1 - 1.3

end{aligned} (3.2) Thus, the definition of solution for system (1.1) is provided.