Existence Theorem for Noninstantaneous Impulsive Evolution Equations

Existence Theorem for Noninstantaneous Impulsive Evolution Equations

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 construct...

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Veröffentlicht in:Journal of mathematics (Hidawi) 2021, Vol.2021, p.1-4
Hauptverfasser: Hina Aslam, Gul I, Ali, Amjad, Rafiq, Maimona
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Banach spaces
Boundary value problems
Existence theorems
Hilbert space
Linear evolution equations
Mathematics
Ordinary differential equations
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Zusammenfassung: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/5539306