We consider the Fife-Greenlee problem $ε^2\triangle u + \bigl(u-\mathbf{a}(y)\bigr)(1-u^2) =0 ~~~ \mbox{in}\ Ω,~~~~~~~\frac{\partial u}{\partialν} = 0 ~~~ \mbox{on}\ \partialΩ,$ where $Ω$ is a bounded domain in ${\mathbb R}^2$ with smooth boundary, $\epsilon>0$ is a small parameter, $ν$ denotes the unit outward normal of $\partialΩ$. Let $Γ = \{y∈ Ω: \mathbf{a}(y) = 0 \}$ be a simple smooth curve intersecting orthogonally with $\partialΩ$ at exactly two points and dividing $Ω$ into two disjoint nonempty components. We assume that $-...
