On a multiplicity result of J. R. Ward for superlinear planar systems

Abstract

The purpose of this paper is to prove, under some assumptions on $g$, that the boundary value problem \begin{gather*} u'= -g(t, u, v)v, \quad v'= g(t, u, v)u, \\ u(0)=0=u(\pi), \end{gather*} has infinitely many solutions. To prove our first main result we use a theorem of J. R. Ward and to prove the second one we use Capietto-Mawhin-Zanolin continuation theorem.