Sentence examples for impulsive terms from inspiring English sources

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.

A solution is called a solution generated by impulses if this solution is non-trivial when impulsive terms are not zero, but it is trivial when impulsive term is 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.

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.

By using the transformation technique to deal with impulsive term of second impulsive differential equations, the authors obtained the existence results of positive solutions by using fixed point theorems in a cone.