Existence Theorem for Noninstantaneous Impulsive Evolution Equations - Gul I Hina Aslam; Amjad Ali; Maimona Rafiq (Journal of Mathematics)
In this note, the variational form of the classical Lax–Milgram theorem is used for the divulgence of variational structure of the first-order noninstantaneous impulsive linear evolution equation. The existence and uniqueness of the weak solution of the problem is obtained. In future, this constructive theory can be used for the corresponding semilinear problems.