Graduate School of Science and Engineering, Mathematics, Physics, and Earth Sciences, Graduate School of Science and Engineering Mathematics,Physics, and Earth Sciences

Journal of Differential Equations 257 2430-2463 Oct 2014 [Refereed]

We consider the semilinear elliptic equation δu+K(|x|)up=0 in RN for N>2 and p>1, and study separation phenomena of positive radial solutions. With respect to intersection and separation, we establish a classification of the solution structures, a...

International Journal of Differential Equations 2013 Nov 2013 [Refereed]

We study a new kind of asymptotic behaviour near t = 0 for the nonautonomous system of two linear differential equations: x ' (t) = A (t) x (t), t ε (0, t0], where the matrix-valued function A = A (t) has a kind of singularity at t = 0. It is call...

Communications on Pure and Applied Analysis 12 1861-1880 Sep 2013 [Refereed]

In this paper, we consider solutions to a Cauchy problem for a parabolic-elliptic system in two dimensional space. This system is a simplified version of a chemotaxis model, and is also a model of self-interacting particles. The behavior of soluti...

Journal of Differential Equations 253 3029-3060 Dec 2012 [Refereed]

We consider the Cauchy problem, where N>2, p>1, and u 0 is a bounded continuous non-negative function in R N. We study the case where u 0(x) decays at the rate |x| -2/(p-1) as |x|→∞, and investigate the stability and instability properties of forw...

Discrete and Continuous Dynamical Systems 32 3691-3713 Jul 2012 [Refereed]

We consider a parabolic-elliptic system of equations that arises in modelling the chemotaxis in bacteria and the evolution of self-attracting clusters. In the case space dimension 3 ≤ N ≤ 9, we will derive criteria of the blow-up rate of solutions...

Bulletin of the London Mathematical Society 44 545-562 Jun 2012 [Refereed]

We consider conditionally oscillatory second-order linear differential equations with a parameter, and investigate the asymptotic behaviour and number of zeros of solutions to the equations. In particular, we find criteria for the equations to be ...