Mixed states for an Allen-Cahn type equation. II
The authors deal with the existence of multibump solutions for an Allen-Cahn equation: \[ -\Delta u+F_u'(x,y,u)=0,\tag{1} \] where \((x,y) \in\mathbb R^2\) and \(F\) is a given function. Under some suitable assumptions on \(F\), that is, by eliminating a strong spatial reversibility condition and by weakining certain nondegeneracy conditions on families of basic heteroclinic solutions, the authors using novel minimization arguments establish the existence of multibump solutions.
scientific article; zbMATH DE number 2113881