Stable and Unstable Manifolds for Non-Linear Elliptic Equations with Parameter.
Abstract:
The paper is devoted to investigating the Cauchy problem for non-linear elliptic equations with parameter. It is proved that there exist two analytic manifolds M+ and M- embedded into the phase space E of the equation in question such that the Cauchy problem with initial data on M± has a unique solution belonging to the Sobolev space. Moreover, these manifolds intersect only at the origin, and the direct sum of the tangent spaces to M+ and M- at this point coincides with E.
Publication language:russian
Research direction:
Mathematical problems and theory of numerical methods
