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

• Autorzy: Nguyen Thieu Huy , Ngo Quy Dang
• Języki publikacji: 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.

Kategorie tematyczne

• 35B10: Periodic solutions
• 35B35: Stability
• 34D20: Stability
• 34C25: Periodic solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2016
• Tom: 116
• Numer: 2
• Strony: 173-195

Daty

wydano

2016

Twórcy

autor

Nguyen Thieu Huy

• 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

Ngo Quy Dang

• Thai Binh College of Education, and Training, Cao Dang Su Pham Thai Binh, Chu Van An, Quang Trung, Thai Binh, Vietnam

Identyfikatory

DOI

10.4064/ap3677-10-2015