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- W1997507296 abstract "This paper concerns the existence and asymptotic characterization of saddle solutions in $${mathbb {R}^{3}}$$ for semilinear elliptic equations of the form $$-Delta u + W'(u) = 0,quad (x, y, z) in {mathbb {R}^{3}} qquadqquadqquad (0.1)$$ where $${W in mathcal{C}^{3}(mathbb {R})}$$ is a double well symmetric potential, i.e. it satisfies W(−s) = W(s) for $${s in mathbb {R},W(s) > 0}$$ for $${s in (-1,1)}$$ , $${W(pm 1) = 0}$$ and $${W''(pm 1) > 0}$$ . Denoted with $${theta_{2}}$$ the saddle planar solution of (0.1), we show the existence of a unique solution $${theta_{3} in {mathcal{C}^{2}}(mathbb {R}^{3})}$$ which is odd with respect to each variable, symmetric with respect to the diagonal planes, verifies $${0 < theta_{3}(x,y,z) < 1}$$ for x, y, z > 0 and $${theta_{3}(x, y, z) to_{z to + infty} theta_{2}(x, y)}$$ uniformly with respect to $${(x, y) in mathbb {R}^{2}}$$ ." @default.
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- W1997507296 date "2012-11-23" @default.
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- W1997507296 title "Saddle solutions for bistable symmetric semilinear elliptic equations" @default.
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- W1997507296 doi "https://doi.org/10.1007/s00030-012-0210-1" @default.
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