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Boundedness results of solutions to the equation x ′′′ + a x ′′ + g ( x ) x + h ( x ) = p ( t ) without the hypothesis h ( x ) sgn x 0 f o r | x | > R .

Ján Andres (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi h ( x ) sgn x 0 f o r ...

Bounds of the matrix eigenvalues and its exponential by Lyapunov equation

Guang-Da Hu, Taketomo Mitsui (2012)

Kybernetika

We are concerned with bounds of the matrix eigenvalues and its exponential. Combining the Lyapunov equation with the weighted logarithmic matrix norm technique, four sequences are presented to locate eigenvalues of a matrix. Based on the relations between the real parts of the eigenvalues and the weighted logarithmic matrix norms, we derive both lower and upper bounds of the matrix exponential, which complement and improve the existing results in the literature. Some numerical examples are also...

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