Qualitative Properties of Saddle-Shaped Solutions to Bistable Diffusion Equations
نویسندگان
چکیده
منابع مشابه
Qualitative Properties of Saddle-shaped Solutions to Bistable Diffusion Equations
We consider the elliptic equation −∆u = f(u) in the whole R , where f is of bistable type. It is known that there exists a saddleshaped solution in R. This is a solution which changes sign in R and vanishes only on the Simons cone C = {(x, x) ∈ R×R : |x| = |x|}. It is also known that these solutions are unstable in dimensions 2 and 4. In this article we establish that when 2m = 6 every saddle-s...
متن کاملSaddle-shaped Solutions of Bistable Diffusion Equations in All of R
We study the existence and instability properties of saddleshaped solutions of the semilinear elliptic equation −∆u = f(u) in the whole R, where f is of bistable type. It is known that in dimension 2m = 2 there exists a saddle-shaped solution. This is a solution which changes sign in R and vanishes only on {|x1| = |x2|}. It is also known that this solution is unstable. In this article we prove ...
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We establish existence and qualitative properties of saddle-shaped solutions of the elliptic fractional equation (−∆)u = f(u) in all the space R, where f is of bistable type. These solutions are odd with respect to the Simons cone and even with respect to each coordinate. More precisely, we prove the existence of a saddle-shaped solution in every even dimension 2m, as well as its monotonicity p...
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ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2010
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2010.484039