two-point boundary value problems for a class of second-order ordinary differential equations

ู…ุณุงุฆู„ ุงู„ู‚ูŠู…ุฉ ุงู„ุญุฏูŠุฉ ุนู†ุฏ ู†ู‚ุทุชูŠู† ู„ูุฆุฉ ู…ู† ุงู„ู…ุนุงุฏู„ุงุช ุงู„ุชูุงุถู„ูŠุฉ ุงู„ุนุงุฏูŠุฉ ู…ู† ุงู„ุฑุชุจุฉ ุงู„ุซุงู†ูŠุฉ

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ID: 220649
2012
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Abstract
We study the general semilinear second-order ODE ๐‘ข๎…ž๎…ž+๐‘”(๐‘ก,๐‘ข,๐‘ข๎…ž)=0 under different two-point boundary conditions. Using the method of upper and lower solutions, we obtain an existence result. Moreover, under a growth condition on ๐‘”, we prove that the set of solutions of ๐‘ข๎…ž๎…ž+๐‘”(๐‘ก,๐‘ข,๐‘ข๎…ž)=0 is homeomorphic to the two-dimensional real space.
ู†ุฏุฑุณ ุงู„ู…ุนุงุฏู„ุฉ ุงู„ุชูุงุถู„ูŠุฉ ุงู„ุนุงุฏูŠุฉ ุดุจู‡ ุงู„ุฎุทูŠุฉ ุงู„ุนุงู…ุฉ ู…ู† ุงู„ุฑุชุจุฉ ุงู„ุซุงู†ูŠุฉ ๐‘ข๎…ž๎…ž+๐‘”(๐‘ก,๐‘ข,๐‘ข๎…ž)=0 ููŠ ุธู„ ุดุฑูˆุท ุญุฏูŠุฉ ุซู†ุงุฆูŠุฉ ุงู„ู†ู‚ุทุฉ ู…ุฎุชู„ูุฉ. ูˆุจุงุณุชุฎุฏุงู… ุทุฑูŠู‚ุฉ ุงู„ุญู„ูˆู„ ุงู„ุนู„ูŠุง ูˆุงู„ุฏู†ูŠุงุŒ ู†ุญุตู„ ุนู„ู‰ ู†ุชูŠุฌุฉ ูˆุฌูˆุฏ. ุนู„ุงูˆุฉ ุนู„ู‰ ุฐู„ูƒุŒ ูˆุชุญุช ุดุฑุท ู†ู…ูˆ ู…ูุฑูˆุถ ุนู„ู‰ ๐‘”ุŒ ู†ุซุจุช ุฃู† ู…ุฌู…ูˆุนุฉ ุญู„ูˆู„ ๐‘ข๎…ž๎…ž+๐‘”(๐‘ก,๐‘ข,๐‘ข๎…ž)=0 ู…ุชุดุงูƒู„ุฉ ุทูˆุจูˆู„ูˆุฌูŠุงู‹ (ู‡ูˆู…ูŠูˆู…ูˆุฑููŠุฉ) ู…ุน ุงู„ูุถุงุก ุงู„ุญู‚ูŠู‚ูŠ ุซู†ุงุฆูŠ ุงู„ุฃุจุนุงุฏ.
Reference Key
sengupta2012internationaltwo-point Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors
Journal structural engineering and mechanics
Year 2012
DOI
10.1155/2012/794040
URL
Keywords

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