Sentence examples for a singular system for from inspiring English sources
Property 3 follows from the first two properties: The compactness of H ij, established in Property 1, implies the existence of a singular system, since there exists a singular system for any compact operator (see Section 16.1 of [32]).
The coefficients of the cubic terms are also uniquely calculated, except for the term w 2 w ¯, whose coefficient satisfies a singular system for ( i α I 3 − A ) h 21 = C ( q, q, q ¯ ) + B ( q ¯, h 20 ) + 2 B ( q, h 11 ) − G 21 q, (2.7).
We know from Lemma 1 that there exists a singular value expansion for H 11, so let (left {sigma _{11}^{ k)}, U_{11}^{ k)}, V_{11}^{ k)}right }_{k=1}^{infty }) be a singular system for the operator (mathsf {H}_{11}: mathcal {T}_{1}rightarrow mathcal {R}_{1}) (see Lemma 5 in Appendix B for the definition of a singular system).
For a singular system, there are few articles considering finite-time control.
Exploiting Amann type three solutions theorem for a singular system, we prove the existence, nonexistence, and multiplicity of positive solutions when nonlinear terms have a combined sublinear effect at ∞. MSC 35J55, 34B18.
There exists a singular system {σ k,v k,u k }, for C defined as follows.
A singular system provides a suitable way to handle such problems, the robust control theory based on singular system models has been widely developed for many years.
In this paper, we generalize the results studied in [25, 26] to the following more general singular system for three-point nonlocal BVPs: (1.3).
See Lemma 5 in Appendix B for a description of the properties of singular systems for compact operators, or see Section 2.2 of [33] or Section 16.1 of [32] for a thorough treatment.
It is proved that the bounded real lemma for discrete singular system can be described by a strict matrix inequality.
We study the sufficient conditions for existence of positive solution for the singular system (1.3) under weaker hypothesis on and as compared to the previously studied results.
