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- W1994733495 abstract "We consider the sufficiency of the Matkowsky condition concerning the differential equation $varepsilon y'' + f(x,varepsilon )yâ + g(x,varepsilon )y = 0;( - a leqslant x leqslant b)$ under the assumption that $f(0,varepsilon ) = 0$ identically in $varepsilon ,{f_x}(0,varepsilon ) ne 0$ with $f > 0$ for $x < 0$ and $f < 0$ for $x > 0$. Y. Sibuya proved that the Matkowsky condition implies resonance in the sense of N. Kopell if $f$ and $g$ are convergent power series for $|varepsilon | < rho ;(rho > 0),f(x,0)=-2x$ and the interval $[ - a,b]$ is contained in a disc $D$ with center at $0$. The main problem in this work is to remove from Sibuyaâs result the assumption that $D$ is a disc." @default.
- W1994733495 created "2016-06-24" @default.
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- W1994733495 date "1983-02-01" @default.
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- W1994733495 title "The sufficiency of the Matkowsky condition in the problem of resonance" @default.
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- W1994733495 doi "https://doi.org/10.1090/s0002-9947-1983-0701516-5" @default.
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