Sentence examples for a variational setting for from inspiring English sources

First, we introduce a variational setting for problem (P).

In this section, we establish a variational setting for the system (VS).

The assessment is performed mathematically, through an examination of the variational setting for the least-squares formulation of an abstract nonlinear boundary-value problem, and also computationally, through the numerical simulation of the least-squares finite element solutions of both a nonlinear form of the Poisson equation and also the incompressible Navier Stokes equations.

Now we establish the variational setting for our problem (1).

In this section, we give the variational setting for (1.1) and some related preliminary lemmas.

In this section, we give some preliminary lemmas and the variational setting for (1.1).

In this section, we establish the variational setting for our problem and give the variant fountain theorem.

Second, the variational setting for our problem is more complex and different from the case where (V=1) since the potential V is a general periodic function.

In order to prove our main results, we first give some properties of space X on which the variational setting for problem (1.1) is defined.

Indeed, it is worth observing that the adequate variational setting for the second order equation biggl(frac{u'}{sqrt{1+u^{prime2}}} biggr)' = -f u) (33) is the space of bounded variation functions.

Recently, Jiao and Zhou [36] introduced some appropriate function spaces as their working space and set up a variational functional for the following system: { − d d t ( 1 2 0 D t − β ( u ′ ( t ) ) + 1 2 t D T − β ( u ′ ( t ) ) ) = ∇ F ( t, u ( t ) ), a.e.  t ∈ [ 0, T ], u ( 0 ) = u ( T ) = 0, (1.2).