In this paper we establish some new oscillation criteria for a second order nonlinear delay differential equation of Emden–Fowler type with damping term. These results extend and improve some of the well-known results in the nondelay case. Our results in the delay case are new and can be applied to new classes of equations which are not covered by the known criteria for oscillation. Some select...

We consider weak positive solutions of the equation −∆mu = f(u) in the halfplane with zero Dirichlet boundary conditions. Assuming that the nonlinearity f is locally Lipschitz continuous and f(s) > 0 for s > 0, we prove that any solution is monotone. Some Liouville type theorems follow in the case of Lane-Emden-Fowler type equations. Assuming also that |∇u| is globally bounded, our result impli...

arises in the study of gas dynamics and fluids mechanics, and in the study of relativistic mechanics, nuclear physics, and chemically reacting system see, e.g., 1 and the references therein for the continuous model. The negative exponent Emden-Fowler equation α < 0 has been used in modeling non-Newtonian fluids such as coal slurries 2 . The physical interest lies in the existence of positive so...

We study the Emden-Fowler equation −∆u = |u|u on the hyperbolic space H . We are interested in radial solutions, namely solutions depending only on the geodesic distance from a given point. The critical exponent for such equation is p = (n + 2)/(n − 2) as in the Euclidean setting, but the properties of the solutions show striking differences with the Euclidean case. While the papers [23, 4] con...

Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent standard software packages are available for ODEs, there are for good reasons no standard numerical continuation toolboxes available for parti...