Asymptotic expansions about infinity for solutions of nonlinear differential equations with coherently decaying forcing functions

• Autores: Luan Hoang
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 25, Nº 1, 2024, págs. 311-370
• Idioma: inglés
• DOI: 10.2422/2036-2145.202109_004
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• Resumen

  • This paper studies, in fine details, the long-time asymptotic behav- ior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions de- cay, as time tends to infinity, in a coherent way expressed by combinations of the exponential, power, logarithmic and iterated logarithmic functions. The de- cay may contain sinusoidal oscillations not only in time but also in the logarithm and iterated logarithm of time. It is proved that the decaying solutions admit cor- responding asymptotic expansions, which can be constructed concretely. In the case of the real Euclidean spaces, the real-valued decaying solutions are proved to admit real-valued asymptotic expansions. Our results unite and extend the theory investigated in many previous works.