×

Existence of positive solutions for non local \(p\)-Laplacian thermistor problems on time scales. (English) Zbl 1136.34305

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)

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
PDFBibTeX XMLCite
Full Text: arXiv EuDML EMIS