%0 Journal Article
%T Admissible inertial manifolds for second order in time evolution equations
%J Khayyam Journal of Mathematics
%I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
%Z 2423-4788
%A Le, Anh Minh
%D 2020
%\ 07/01/2020
%V 6
%N 2
%P 155-173
%! Admissible inertial manifolds for second order in time evolution equations
%K Admissible inertial manifolds
%K second order in time evolution equations
%K admissible function spaces
%K Lyapunov--Perron method
%R 10.22034/kjm.2020.109813
%X We prove the existence of admissible inertial manifolds for the second order in time evolution equations of the form $$ ddot{x}+2varepsilon dot{x}+Ax=f(t,x)$$ when $A$ is positive definite and self-adjoint with a discrete spectrum and the nonlinear term $f$ satisfies the $varphi$-Lipschitz condition, that is, $|f(t,x)-f(t,y)|leqslantvarphi(t)left |A^{beta}(x-y)right |$ for $varphi$ belonging to one of the admissible Banach function spaces containing wide classes of function spaces like $L_{p}$-spaces, the Lorentz spaces $L_{p,q}$, and many other function spaces occurring in interpolation theory.
%U http://www.kjm-math.org/article_109813_372333a09954785108dc346740036a94.pdf