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Zbl 1169.39007
Zhao, Xiangkui; Ge, Weigao
Multiple positive solutions for time scale boundary value problems on infinite intervals.
(English)
[J] Acta Appl. Math. 106, No. 2, 265-273 (2009). ISSN 0167-8019; ISSN 1572-9036/e

Consider the time-scale boundary value problems $$(\phi _{p}(u^{\Delta }(t)))^{\nabla }+q(t)f(u(t),u^{\Delta }(t))=0,\quad t\in (0,\infty)_{T}$$ $$u(0)=\beta u^{\Delta }(\eta )~,\quad \lim_{t\in \Bbb{T},~t\to \infty}u^{\Delta }(t)=0,$$ where $\Bbb{T}$ is a time scale. By means of Leggett-Williams fixed point theorem, the authors establish sufficient conditions that guarantee the existence of at least three positive solutions to the above boundary value problem.
[Fozi Dannan (Damascus)]
MSC 2000:
*39A11 Stability of difference equations
39A12 Discrete version of topics in analysis
34B15 Nonlinear boundary value problems of ODE

Keywords: time scale; positive solutions; infinite intervals; multiple solutions; Leggett-Williams fixed point theorem

Cited in: Zbl 1190.39005

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