## Existence theory for positive solutions to one-dimensional $$p$$-Laplacian boundary value problems on time scales.(English)Zbl 1139.34047

This paper studies the boundary value problem
$\left(\phi_p \left(u^{\triangle}(t)\right)\right)^{\triangle} + h(t) f(u(\sigma(t)) = 0, \quad t \in [a,b],$
$u(a) - B_0\left(u^{\triangle}(a)\right) = 0, \quad u^{\triangle}\left(\sigma(b)\right) = 0,$
where $$\phi_p(u)$$ is the $$p$$-Laplacian operator. The problem is considered on a time scale. Using fixed point theorems of Krasnosel’skii, Avery and Henderson, and Leggett and Williams, the authors obtain several existence and multiplicity results for positive solutions.

### MSC:

 34K10 Boundary value problems for functional-differential equations 39A10 Additive difference equations

### Keywords:

time scales; positive solution; cone; fixed point
Full Text:

### References:

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