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arXiv:2404.11697v1 Announce Type: new
Abstract: The goal of this paper is to investigate the existence of saddle solutions for some classes of elliptic partial differential equations of the Allen-Cahn type, formulated as follows:
\begin{equation*}
-div\left(\frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right) + A(x,y)V'(u)=0~~\text{ in }~~\mathbb{R}^2.
\end{equation*}
Here, the function $A:\mathbb{R}^2\to\mathbb{R}$ exhibits periodicity in all its arguments, while $V:\mathbb{R}\to\mathbb{R}$ characterizes a double-well symmetric potential with minima at $t=\pm\alpha$.
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