The ground state of the energy super-critical Gross–Pitaevskii equation with a harmonic potential converges in space to singular solution limit large amplitudes. can be represented by curve which has either oscillatory or monotone behavior, depending on dimension system and power focusing nonlinearity. We address here case for cubic nonlinearity spatial dimensions d≥13. By using shooting method...

We consider a nonlinear transport equation as a hyperbolic generalisation of the well-known reaction diiusion equation. We show the existence of strictly monotone travelling fronts for the three main types of the nonlinearity: the positive source term, the combustion law, and the bistable case. In the rst case there is a whole interval of possible speeds containing its strictly positive minimum...

We consider a nonlinear transport equation as a hyperbolic generalisation of the well-known reaction diffusion equation. Themodel is based on earlier work of K.P. Hadeler attempting to include run-and-tumble motion into the mathematical description. Previously, we proved the existence of strictly monotone travelling fronts for the three main types of the nonlinearity: the positive source term, ...

In this paper, we study the traveling front solutions of the LotkaVolterra competition-diffusion system with bistable nonlinearity. It is wellknown that the wave speed of traveling front is unique. Although little is known for the sign of the wave speed. In this paper, we first study the standing wave which gives some criteria when the speed is zero. Then, by the monotone dependence on paramete...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

We establish a criterion for the global exponential stability of the zero solution of the scalar retarded functional differential equation x (t) = L(x t) + g(t,x t) whose linear part y (t) = L(y t) generates a monotone semiflow on the phase space C = C([−r,0],R) with respect to the exponential ordering, and the nonlinearity g has at most linear growth.

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...

The number of correctable/uncorrectable errors of weight half the minimum distance plus one for the first-order Reed-Muller codes is determined. From a cryptographic viewpoint, this result immediately leads to the exact number of Boolean functions of m variables with nonlinearity 2m−2 + 1. The notion of larger half and trial set , which is introduced by Helleseth, Kløve, and Levenshtein to desc...

Dual minimum principles for displacements and stresses are well established for linear variational problems and also for nonlinear (and monotone) constitutive laws. This paper studies the problem of geometric nonlinearity. By introducing a gap function, we recover complementary variational principles in the equilibrium problems of mathematical physics. When the gap function is nonnegative those...

Abstract. Convergence of a full discretization is shown for a general class of nonlinear parabolic November 10, 2011 problems. The numerical method combines the backward Euler method for the time discretization with a generalized internal approximation scheme for the spatial discretization. The governing monotone elliptic differential operator is described by a nonlinearity that may have anisot...