Existence of positive solutions of $$p$$-Laplacian difference equations.(English)Zbl 1125.39007

Using a fixed point theorem, the authors give conditions for the existence of at least two positive solutions for boundary value problem $$\Delta u(0) = u(T+2) = 0$$ of the $$p$$-Laplacian difference equation
$\Delta [\phi_p(\Delta u(t-1))] + a(t)f(u(t)) = 0, \quad t \in \{1,\dots, T+1\},$
where $$\phi_p(s) = | s| ^{p-2}s, \;p > 1,$$ the function $$f: \mathbb R^+ \to\mathbb R^+$$ is continuous and $$a(t)$$ is a positive valued function defined on $$\{1,\dots, T+1\}.$$

MSC:

 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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References:

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