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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2016 | 116 | 2 | 173-195

## Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces

EN

### Abstrakty

EN
We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence, uniqueness and conditional stability of periodic solutions to the above semilinear equation in the case that the family $(A(t))_{t≥0}$ generates an evolution family having an exponential dichotomy. We also prove the existence of a local stable manifold near the periodic solution in that case.

173-195

wydano
2016

### Twórcy

autor
• School of Applied Mathematics, and Informatics, Hanoi University of Science and Technology, Vien Toan ung dung va Tin hoc, Dai hoc Bach khoa Hanoi, 1 Dai Co Viet, Hanoi, Vietnam
autor
• Thai Binh College of Education, and Training, Cao Dang Su Pham Thai Binh, Chu Van An, Quang Trung, Thai Binh, Vietnam