Nonoscillatory solutions for the one-dimensional \(p\)-Laplacian (Q1298805)

The author studies the existence of nonoscillatory solutions of the equation \[ \Delta \Phi(\Delta x_{k-1})+f(k,x_k)=0,\quad k=1,2,\cdots \] where \(\Phi:R\rightarrow R\) is defined by \(\Phi(s)=|s|^{p-1}s\) (\(p>1\) fixed), \(f:N\times R\rightarrow R^+\) and \(\{x_k\}_1^\infty\) is a nonnegative sequence with infinitely many positive terms.