Positive solutions of nonlinear elliptic equations in unbounded domains in \(\mathbb{R}^2\) (Q1398031)

The authors prove the existence of infinitely many positive solutions of the nonlinear equation \(\Delta u+f(.,u)=0\) in \(D\) with \(u=0\) on \(\partial D\), where \(D\) is an unbounded domain in \(\mathbb{R}^2\) with a compact nonempty boundary \(\partial D\) consisting of finitely many Jordan curves.