Bifurcation at multiple eigenvalues and stability of bifurcating solutions

摘要: If K is a bounded linear operator from the real Banach space U into V and ƒ:U×R→V has value zero at (0, 0), existence stability of equilibrium solutions dynamical system K dudt = ƒ(u, α) which are close to origin in U×R studied. It assumed that ƒu(0, 0): → Freholm index zero. The only restriction on dimension null 0) order vanishing, ƒ restricted Dƒ(0,0):U×R→V, they both be finite positive integers. main result gives conditions under which equation, determines neighborhood origin, also these solutions.