Sentence examples for associated to the problems from inspiring English sources

6 are presented for energy solutions, that is for solutions belonging to the natural energy space W 1, p associated to the problems considered.

In several papers, to establish characterizations of solution sets of inequality constrained programming problems, Lagrange functions which were associated to the problems were proved to be constant on their optimal solution sets [1 5].

We design an algorithm that solves numerically the Euler Lagrange equations associated to the problem.

In Figure 10 we plot the lower bound of the coercivity constant of the bilinear form associated to the problem.

We prove the existence of pullback attractors for the dynamical system associated to the problem under more general assumptions.

We present a new approach that is based on the introduction of a natural constraint associated to the problem.

Section 4 gets that the functional associated to the problem possesses the mountain geometry structure, and the last section concludes the proof of the main result.

The role of (AR) is to ensure the boundness of the Palais-Smale sequences for the Euler-Lagrange functional associated to the problem.

This technique will be applied as a systematic procedure to obtain the Eshelby's energy momentum tensor associated to the problem under consideration.

We have associated to the problem under consideration the operator polynomial L lambda)=lambda^{2}M-ialphalambda K-A, (1.2) where (alpha>0), while M and K are self-adjoint operators.

Our goal is to solve, by discretization, a singular boundary integral equation associated to the problem, and to obtain the numerical solution of the problem with a computer code made in Mathcad, based on this approach.