Existence, uniqueness and global behavior of the solutions to some nonlinear vector equations in a finite dimensional Hilbert space

Abstract

The initial value problem and global properties of solutions are studied for the vector equation: $\Big(\|u'\|^{l}u'\Big)'+\|A^{\frac{1}{2}}u\|^\beta Au+g(u')=0$ in a finite dimensional Hilbert space under suitable assumptions on $g$.