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Multiple positive solutions for time scale boundary value problems on infinite intervals. (English) Zbl 1169.39007
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.

39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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