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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

${\left({\phi }_{p}\left({u}^{{\Delta }}\left(t\right)\right)\right)}^{\nabla }+q\left(t\right)f\left(u\left(t\right),{u}^{{\Delta }}\left(t\right)\right)=0,\phantom{\rule{1.em}{0ex}}t\in {\left(0,\infty \right)}_{T}$
$u\left(0\right)=\beta {u}^{{\Delta }}\left(\eta \right)\phantom{\rule{3.33333pt}{0ex}},\phantom{\rule{1.em}{0ex}}\underset{t\in 𝕋,\phantom{\rule{3.33333pt}{0ex}}t\to \infty }{lim}{u}^{{\Delta }}\left(t\right)=0,$

where $𝕋$ 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.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 34B15 Nonlinear boundary value problems for ODE
##### References:
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