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Zbl 1156.34308
Sidi Ammi, Moulaz Rchid; Torres, Delfim F.M.
Existence of infinitely many solutions for a quasilinear elliptic problem on time scales. (English)
[J] Int. J. Pure Appl. Math. 39, No. 2, 239-248 (2007). ISSN 1311-8080

The authors consider the existence of positive solutions for the boundary value problem $$ -\big ( \phi (u^\Delta(t)) \big )^\nabla = f(u(t)) + h(t), \, t \in \mathbb{T},$$ $$ u^\Delta(0) = 0, \quad u(T) - u(\eta) = 0, $$ where $\mathbb{T}$ is a time scale, $0, T \in \mathbb{T}$ and $\phi(s) = \vert s\vert ^{p-2}s, p > 1$. \par This paper contains numerous errors, not the least of which is that the authors failed to invert the operator correctly. Since the arguments in support of their conjectures are faulty, there are no valid results in this manuscript.
[Eric R. Kaufmann (Little Rock)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34B18 Positive solutions of nonlinear boundary value problems
39A10 Difference equations

Keywords: $p$-Laplacian; positive solution; quasilinear; time scales

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