非线性四阶周期边值问题的最优正解

Abstract

Abstract:

The fourth order periodic boundary value problem u⁽⁴⁾-m⁴u+F(t, u(τ(t)))=0, 0<t<2π, with u⁽ⁱ⁾(0)=u⁽ⁱ⁾(2π), i=0,1, 2, 3, is studied by using the fixed point theorem in cones, where F:[0, 2π]×R⁺→ R⁺ and τ: [0, 2τi]→[0, 2π] are continuous and 0<m<1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0, M), where M is the smallest positive root of the equation tan mπ=-tanh mπ, which takes the value 0.7528094 with an error of ±10^-7.

Key words: Positive solutions, Periodic boundary value problem, Fixed point theorem

CLC Number:

34K20

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ZHANG Li-Li. Optimal Positive Solutions of a Nonlinear Fourth Order Periodic Boundary Value Problem[J].Acta mathematica scientia,Series A, 2009, 29(5): 1426-1433.

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Optimal Positive Solutions of a Nonlinear Fourth Order Periodic Boundary Value Problem

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