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Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension $p$ -Laplacian

Daqing Jiang; Li Li Zhang; Donal O'Regan; Ravi P. Agarwal — 2004

Archivum Mathematicum

In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem $\{\begin{matrix} Δ [φ (Δ u (t - 1))] + q (t) f (t, u (t)) = 0, t \in {1, 2, \dots, T} \\ u (0) = u (T + 1) = 0, \end{matrix}$ where $φ (s) = {| s |}^{p - 2} s$ , $p > 1$ and our nonlinear term $f (t, u)$ may be singular at $u = 0$ .

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