Saddle Solutions for Allen–Cahn Type Equations Involving the Prescribed Mean Curvature Operator

Isneri R.J.S.; Torres Ledesma C.E. · Milan Journal of Mathematics (2025) · DOI: 10.1007/s00032-025-00418-y

Resumen

The goal of this work is to investigate the existence of saddle solutions for the following class of elliptic partial differential equations of the Allen–Cahn type (Formula presented.) where the differential operator is the classical prescribed mean curvature operator. Here, the function A:R2→R exhibits periodicity in all its arguments, while V:R→R characterizes a double-well symmetric potential with global minima at t=±α. © The Author(s), under exclusive licence to Seminario Matematico e Fisico di Milano 2025.