Periodic problem for non-instantaneous impulsive partial differential equations

Huanhuan Zhang; Jia Mu; Huanhuan Zhang; Jia Mu

doi:10.3934/math.2022186

AIMS Mathematics

2022, Volume 7, Issue 3: 3345-3359. doi: 10.3934/math.2022186

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Research article

Periodic problem for non-instantaneous impulsive partial differential equations

Huanhuan Zhang ^,,
Jia Mu

College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, 730030, China

Received: 05 September 2021 Accepted: 11 November 2021 Published: 30 November 2021
MSC : 34A37, 34B77, 47D06, 43K13

We obtain a new maximum principle of the periodic solutions when the corresponding impulsive equation is linear. If the nonlinear is quasi-monotonicity, we study the existence of the minimal and maximal periodic mild solutions for impulsive partial differential equations by using the perturbation method, the monotone iterative technique and the method of upper and lower solution. We give an example in last part to illustrate the main theorem.
- non-instantaneous impulses,
- evolution equation,
- periodic mild solution,
- the monotone iterative technique,
- existence
Citation: Huanhuan Zhang, Jia Mu. Periodic problem for non-instantaneous impulsive partial differential equations[J]. AIMS Mathematics, 2022, 7(3): 3345-3359. doi: 10.3934/math.2022186

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Abstract

We obtain a new maximum principle of the periodic solutions when the corresponding impulsive equation is linear. If the nonlinear is quasi-monotonicity, we study the existence of the minimal and maximal periodic mild solutions for impulsive partial differential equations by using the perturbation method, the monotone iterative technique and the method of upper and lower solution. We give an example in last part to illustrate the main theorem.

References

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