Ammi, Moulay Rchid Sidi; Torres, Delfim F. M. Existence of positive solutions for non local \(p\)-Laplacian thermistor problems on time scales. (English) Zbl 1136.34305 JIPAM, J. Inequal. Pure Appl. Math. 8, No. 3, Paper No. 69, 10 p. (2007). The authors study the existence of positive solutions for the nonlocal \(p\)-Laplacian thermistor problem on a time scale \(\mathbb{T}:\) \[ -\big( \phi_p(u^\Delta(t))\big)^\nabla=\frac{\lambda f(u(t))}{(\int^T_0 f(u(\tau))\nabla \tau)^k},\quad t\in (0,T)_{\mathbb{T}}, \]\[ \phi_p(u^\Delta(0))-\beta \phi_p(u^\Delta(\eta))=0,\quad u(T)-\beta u(\eta)=0, \]where \(\phi_p(s)=| s| ^{p-2}s\), \(p>1\), \(f:(0,T)_{\mathbb{T}}\rightarrow \mathbb{R}^{+*}\) is continuous. The main tool they used is the Guo-Krasnoselskii fixed point theorem on cones. Reviewer: Ruyun Ma (Lanzhou) Cited in 5 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 39A10 Additive difference equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:Positive solutions; p-Laplacian thermistor problem; time scale; cones PDFBibTeX XMLCite \textit{M. R. S. Ammi} and \textit{D. F. M. Torres}, JIPAM, J. Inequal. Pure Appl. Math. 8, No. 3, Paper No. 69, 10 p. (2007; Zbl 1136.34305) Full Text: arXiv EuDML EMIS