In this paper we study the existence of solutions for the nonlinear elliptic system ⎪⎪⎨ ⎪⎪⎩ Δu−Δu+V1(x)u = fu(x,u,v), Δv−Δv+V2(x)v = fv(x,u,v), u,v ∈ H(R) x ∈ R , where V1(x) and V2(x) are positive continue functions. Under some assumptions on fu(x,u,v) and fv(x,u,v) , we prove the existence of many nontrivial high and small energy solutions by variant Fountain theorems. This generalizes the re...

We consider a homoclinic orbit to saddle fixed point of an arbitrary \begin{document}$ C^\infty $\end{document} map id="M2">\begin{document}$ f on id="M3">\begin{document}$ \mathbb{R}^2 and study the phenomenon that id="M4">\begin{document}$ has infinite family asymptotically stable, single-round periodic...