On Quasicenter Manifolds of Semilinear Equations in Banach Spaces
Copyright policy )On Quasicenter Manifolds of Semilinear Equations in Banach Spaces
In the usual proof of the existence of a center manifold through an equilibrium point of an autonomous semilinear differential equation one needs a \(C^ 1\) bump function on a subspace of the Banach space (called property \(P_ 1\) here). Not every Banach space admits a \(C^ 1\) bump function. By using Lipschitz instead of \(C^ 1\) considerations it is proved here that with suitable conditions a so-called quasicenter manifold always exists, without any restriction on the Banach spaces involved.
Banach space, Equations in function spaces; evolution equations, Nonlinear ordinary differential equations and systems, Nonlinear differential equations in abstract spaces, first order differential equations, equilibrium point, center manifold, bump function, quasicenter manifold, quasilinear differential equation, Manifolds of solutions of ODE, Periodic solutions to ordinary differential equations
Banach space, Equations in function spaces; evolution equations, Nonlinear ordinary differential equations and systems, Nonlinear differential equations in abstract spaces, first order differential equations, equilibrium point, center manifold, bump function, quasicenter manifold, quasilinear differential equation, Manifolds of solutions of ODE, Periodic solutions to ordinary differential equations
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