Sentence examples for impulsive term from inspiring English sources

The periodic impulsive term is clearly observable in both plots.

The approach to deal with the impulsive term is different from earlier approaches.

The method to deal with the impulsive term in the proof of Theorem 6.1 is different from that in the proof of Theorem 3.1.

The compactness condition of the impulsive term, some restrictive conditions on a priori estimation and noncompactness measure estimation have been deleted.

Using a fixed point theorem of cone expansion and compression of norm type and a new method to deal with the impulsive term, we prove that the second-order singular impulsive Neumann boundary value problem has denumerably many positive solutions.

The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensively in the literature.

Consequently, the ensured weak solutions for the problem (1) when (hequiv0) in Theorems 3.1 and 3.2 and in Corollary 3.3 are generated by impulses when impulsive terms (f_{k},g_{k}neq0) for some (1leq kleq m), as well as for the problem (11) when (hequiv0) in Corollary 3.4 are generated by impulses when impulsive terms (f_{1},g_{1},g_{).

Definition 1.2 A solution for problem ( P p, μ ) is said to be generated by impulses if this solution emerges when impulsive terms are not zero, but disappears when impulsive terms are zero.

We say that a solution of the problem (1) is called a solution generated by impulses if this solution is nontrivial when impulsive terms (f_{k},g_{k}neq0) for some (1leq kleq m), but it is trivial when impulsive terms are zero.

More important, the impulsive terms are different from those of papers [8, 9].

Examples to show the bounds of solutions of a partial differential equation with impulsive terms are also given, which cannot be estimated by Gallo and Piccirllo's results.