Sentence examples for first order problem from inspiring English sources

After proving the general result for the n th order case, we concentrate our work in the first order problem u ′ ( t ) + a u ( − t ) + b u ( t ) = h ( t ), for a.e.  t ∈ R ; u ( t 0 ) = c, (2.5).

According to the best of our knowledge, this paper is the first one to treat the periodic first order problem at resonance with external forces and impulses satisfying the Landesman-Lazer type conditions (see (3 - 7) below and compare with conditions in [17]).

In fact, on the one hand the first order problem (where (y=u^{prime2})) begin{cases} y'= -2(A sqrt{y} + Bsin u), y(pi =0,qquad y u) > 0 quad text{for } u neqpi, end{cases} has the nonnegative lower solution (y u)=2B(1+cos u)), so that (bar{y} u)) is always defined and increasing and corresponds to a rotation type motion.

In these scenarios, the practitioners nearly always chose to fix and forget or to engage in first order problem solving.

In other studies, definitions offered for first order problem solving and deviations matched our definition of workarounds [ 24, 58, 59, 73].

This aligns directly with first order problem solving (fixing and forgetting), to the exclusion of second order problem solving (fixing and reporting).

In the literature, there are very few results establishing the existence of more than one solution to first order problems.

Furthermore, asymptotic properties and boundedness of the solutions of initial first order problems are studied in [9] and [10], respectively.

The model consists of a nonlinear fourth order problem with a pointwise isometry constraint, which we discretize with Kirchhoff quadrilaterals.

The self-adjoint sixth order problem [8], the self-adjoint higher order problems [9] and the fourth order Birkhoff regular problems [10] also have the same type of boundary conditions described above.

In this section we are interested in the implementation of the mortar method for the Strang and Fix algorithm in the case of a fourth order problem.