Geodesic
Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension $p$-Laplacian
Archivum mathematicum, Tome 40 (2004) no. 4, pp. 367-381.

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In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem \[ \left\lbrace \begin{array}{l} \Delta \big [\phi (\Delta u(t-1))\big ]+ q(t) f(t,u(t))=0\,,\quad t\in \lbrace 1,2,\dots ,T\rbrace \\[3pt] u(0)=u(T+1)=0\,, \end{array} \right. \] where $\phi (s) = |s|^{p-2}s$, $p>1$ and our nonlinear term $f(t,u)$ may be singular at $u=0$.
Classification : 34B15, 39A11, 39A12
Keywords: multiple solutions; singular; existence; discrete boundary value problem 
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     title = {Existence theory for single and multiple solutions to singular positone discrete {Dirichlet} boundary value problems to the one-dimension $p${-Laplacian}},
     journal = {Archivum mathematicum},
     pages = {367--381},
     publisher = {mathdoc},
     volume = {40},
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     year = {2004},
     mrnumber = {2129959},
     zbl = {1113.39022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2004__40_4_a5/}
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Jiang, Daqing; Zhang, Lili; O'Regan, Donal; Agarwal, Ravi P. Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension $p$-Laplacian. Archivum mathematicum, Tome 40 (2004) no. 4, pp. 367-381. http://geodesic.mathdoc.fr/item/ARM_2004__40_4_a5/