Local structure of bifurcation curves for nonlinear Sturm-Liouville problems

We consider the nonlinear bifurcation problem arising in population dynamics and nonlinear Schrödinger equation:

     

Blow-up with logarithmic nonlinearities

We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition,

     

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms,

     

Short-Time Nonlinear Effects in the Exciton-Polariton System

In the exciton-polariton system, a linear dispersive photon field is coupled to a nonlinear exciton field. Short-time analysis of the lossless system shows that, when the photon field is excited, the time required for that field to exhibit nonlinear effects is longer than the time required for the nonlinear Schrödinger equation, in which the photon field itself is nonlinear. When the initial condition is scaled by \(\epsilon ^\alpha \), it is found that the relative error committed by omitting the nonlinear term in the exciton-polariton system remains within \(\epsilon \) for all times up to \(t=C\epsilon ^\beta \), where \(\beta =(1-\alpha (p-1))/(p+2)\). This is in contrast to \(\beta =1-\alpha (p-1)\) for the nonlinear Schrödinger equation. The result is proved for solutions in \(H^s(\mathbb {R}^n)\) for \(s>n/2\). Numerical computations indicate that the results are sharp and also hold in \(L^2(\mathbb {R}^n)\).     

Existence and asymptotic stability for evolution problems on manifolds with damping and source terms

One considers the nonlinear evolution equation with source and damping terms

     

Oscillations of nonlinear partial difference systems

This paper studies the following two-dimensional nonlinear partial difference systems

     

Asymptotic expansion of the boundary layers of the perturbed simple pendulum problems

We consider the nonlinear eigenvalue problem on an interval

     

Parabolic approach to nonlinear elliptic eigenvalue problems

We consider the asymptotic profiles of the nonlinear parabolic flows ut=Δum to show the geometric properties of the following elliptic nonlinear eigenvalue problems:

     

KAM tori of Hamiltonian perturbations of 1D linear beam equations

In this paper, one-dimensional (1D) nonlinear beam equations

     

Impulsive BVPs with nonlinear boundary conditions for the second order differential equations without growth restrictions

The paper deals with the impulsive nonlinear boundary value problem

     

General theorems for stability and boundedness for nonlinear functional discrete systems

We consider the nonlinear functional discrete system

     

Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials

We establish the existence and multiplicity of semiclassical bound states of the following nonlinear Schrödinger equation:

     

A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions

In this paper, one-dimensional (1D) nonlinear Schrödinger equation

     

Solvability and iterative algorithms for a higher order nonlinear neutral delay differential equation

The paper is concerned with the higher order nonlinear neutral delay differential equation

     

On the Cauchy problem for higher-order nonlinear dispersive equations

We study the higher-order nonlinear dispersive equation