TY - JOUR ID - 109813 TI - Admissible inertial manifolds for second order in time evolution equations JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Le, Anh Minh AD - Department of Mathematical Analysis, Faculty of Natural Sciences, Hongduc University, Thanh Hoa, Vietnam Y1 - 2020 PY - 2020 VL - 6 IS - 2 SP - 155 EP - 173 KW - Admissible inertial manifolds KW - second order in time evolution equations KW - admissible function spaces KW - Lyapunov--Perron method DO - 10.22034/kjm.2020.109813 N2 - We prove the existence of admissible inertial manifolds for the second order in time evolution equations of the form $$ \ddot{x}+2\varepsilon \dot{x}+Ax=f(t,x)$$ when $A$ is positive definite and self-adjoint with a discrete spectrum and the nonlinear term $f$ satisfies the $\varphi$-Lipschitz condition, that is, $\|f(t,x)-f(t,y)\|\leqslant\varphi(t)\left \|A^{\beta}(x-y)\right \|$ 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. UR - https://www.kjm-math.org/article_109813.html L1 - https://www.kjm-math.org/article_109813_372333a09954785108dc346740036a94.pdf ER -