Unbounded solutions of quasi-linear difference equations
The limit behaviour of positive increasing solutions of the difference equation \[ \Delta(a_n\phi_p(\Delta x_n))= b_nf(x_{n+1}) \] with \(\phi_p(u)=| u|^{p-2} u\), \(p> 1\), positive \(a_n\), \(b_n\) and \(uf(u)> 0\) for \(u\neq 0\) is established. Examples are given which show the role of the hypotheses.
scientific article; zbMATH DE number 2082219