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Multiplicity of positive solutions for second-order three-point boundary value problems

โœ Scribed by Ruyun Ma


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
461 KB
Volume
40
Category
Article
ISSN
0898-1221

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We establish the existence of positive solutions for the three-point boundary value problem u" + a(t)f(u) = o, u(0) = 0, u(1) -au(~) = b, where b, c~ > 0, r/ E (0, 1), a~? < 1, are given. Under suitable conditions, we show that there exists a positive number b\* such that the problem has at least on

Multiple positive solutions for second-o
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โœ Xiaoming He; Weigao Ge ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 83 KB

We establish the existence of at least three positive solutions to the second-order three-point boundary value problem, u + f t u = 0 u 0 = 0 ฮฑu ฮท = u 1 , where ฮท 0 < ฮท < 1 0 < ฮฑ < 1/ฮท, and f 0 1 ร— 0 โˆž โ†’ 0 โˆž is continuous. We accomplish this by making growth assumptions on f which can apply to many

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In this paper, we study the existence of positive solutions of a singular three-point boundary value problem for the following second-order differential equation By constructing an available integral operator and combining fixed point index theory with properties of Green's function under some cond

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The existence, nonexistence, and multiplicity of nonnegative solutions are established for the three-point boundary value problem where ฮฒ โˆˆ (0, 1), ฮฑ โˆˆ (0, 1/ฮฒ), and ฮป is a nonnegative parameter, under appropriate hypotheses. The key idea is that the problem of finding a nonnegative solution is tra