Positive solutions of boundary value problems for second-order singular nonlinear differential equations

O175.8; New existence results are presented for the singular second-order nonlinear boundary value problems u" + g(t)f(u) = 0, 0 < t < 1, au(0) - βu′(0) = 0,γu(1) +δu'(l) = 0 under the conditions 0 ≤ fn+ < M1, m1 < f∞-≤∞ or 0 ≤ f∞+<M1, m1 < f 0-≤ ∞, where f +0= limu→of(u)/u, f∞-= limu-→∞(u...

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Veröffentlicht in:Applied mathematics and mechanics 2001-04, Vol.22 (4), p.495-500
Hauptverfasser: Ren-gui, Li, Li-shan, Liu
Format: Artikel
Sprache:eng
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Zusammenfassung:O175.8; New existence results are presented for the singular second-order nonlinear boundary value problems u" + g(t)f(u) = 0, 0 < t < 1, au(0) - βu′(0) = 0,γu(1) +δu'(l) = 0 under the conditions 0 ≤ fn+ < M1, m1 < f∞-≤∞ or 0 ≤ f∞+<M1, m1 < f 0-≤ ∞, where f +0= limu→of(u)/u, f∞-= limu-→∞(u)/u, f0-=limu-→of(u)/u, f+∞= limu→=f(u)/u, g may be singular att = 0 and/ort = 1 . Theproof uses a fixed point theorem in cone theory.
ISSN:0253-4827
1573-2754
DOI:10.1007/BF02438315