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Keywords:
multiple solutions; singular; existence; discrete boundary value problem
multiple solutions; singular; existence; discrete boundary value problem
Summary:
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 $u=0$.
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