Sentence examples for solution for this system from inspiring English sources

Some sufficient conditions are derived for checking the global exponential stability and the existence of periodic solution for this system based on Halanay inequality, mathematical induction and fixed point theorem.

As an example of a case of an asymmetric non-linear restoring force, the forced vibration of a non-linear air spring excited by the motion of the support point is considered, and the characteristic of the stationary solution for this system is analyzed similarly.

With the aid of the solution for this system, which is obtained using the Chebyshev numerical integral technique, such crack tip fracture parameters as the stress intensity factors, the electric displacement intensity factor and the mechanical strain energy release rate are easily evaluated.

By Theorem 1 we conclude that there exists at least one random solution for this system.

We also prove the convergence of a multistep iterative algorithm approximating the solution for this system of variational inclusions.

By using the resolvent technique for the -monotone operators, we prove the existence and uniqueness of solution for this system of variational inclusions.

We also establish the global well-posedness of strong solutions for this system, with any initial data (v0,T0)∈H1∩L∞, such that ∂zv0∈Lm, for some m∈(2,∞), by using the logarithmic type anisotropic Sobolev inequality and a logarithmic type Gronwall inequality.

In this paper, the global exponential stability and periodicity are investigated for a class generalized high-order neural networks with time delays and impulses; some sufficient conditions are derived for checking the global exponential stability and existence of periodic solutions for this system using the generalized Halanay inequality, mathematical induction and a fixed point theorem.

There are multiple solutions for this system of equations.

By using the perturbation method, we establish the existence of both positive and negative solutions for this system.

There have been a lot of excellent results related to the existence and multiplicity of solutions for this system.