Nonlinear Differential Equations by Raimond A. Struble

Author:Raimond A. Struble [Struble, Raimond A.]
Language: eng
Format: epub, pdf
Publisher: INscribe Digital

and the nonlinearity condition (5) may be reformulated as

Then from (44) of Chap. 4, we infer that any solution of (7) satisfies an integral equation of the form

where Y(t) is the principal matrix solution of the associated matrix equation dX/dt = AX and is an initial vector. The hypotheses imply that

for suitable positive constants c and α. Hence

or, what is the same,

But from the nonlinearity condition (8), it follows that there exists a positive number δ such that

for . Then from (10), we have further

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