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Recent papers have studied the existence of phase transition solutions for Allen–Cahn type equations. These solutions are either single or multi-transition spatial heteroclinics or homoclinics between simpler equilibrium states. A sufficient condition for the construction of the multitransition
solutions is that there are gaps in the ordered set of single transition solutions. In this paper we explore the necessity of these gap conditions.
This paper uses minimization methods and renormalized functionals to find spatially heteroclinic solutions for some classes of semilinear elliptic partial differential equations
This paper uses minimization methods and renormalized
functionals to find spatially heteroclinic solutions for some classes
of semilinear elliptic partial differential equations
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