Norimichi Hirano

Existence of limit cycles for coupled van der Pol equations

Abstract In this paper, we consider the existence of limit cycles of coupled van der Pol equations by using S1-degree theory due to Dylawerski et al. (see Ann. Polon. Math. 62 (1991) 243).

Existence of infinitely many solutions for sublinear elliptic problems

Abstract Let N⩾2 and Ω⊂ R N be a bounded domain. In the present paper, we show the existence of infinity many solutions of nonlinear Dirichlet boundary value problem −Δu=g(x,u), u∈H 0 1 (Ω), where g :Ω× R → R is a continuous function satisfying lim|t|→0g(x,t)/t→∞ for all x∈Ω .

Existence of positive solutions for a semilinear elliptic problem with critical Sobolev and Hardy terms

Let N > 4, let 2* = 2N/(N - 2) and let Ω C R N be a bounded domain with a smooth boundary ∂Ω. Our purpose in this paper is to consider the existence of solutions of the problem: u > 0 in Ω, u = 0 on ∂Ω, where 0 < μ< (N-2/2) 2 .

On periodic solutions for forced Van der Pol type equations

In the present paper, we will see that aVan der Pol type equations has aperiodic solution when the forcing term is periodic. By showing the results of some simulations, we illustrate periodicity of the solutions. We also prove that aperiodic solution found near the origin is arepellor.