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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
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