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: $(\Vert u^{\prime }{\Vert }^l{u}^{\prime }{)}^{\prime }+\Vert A^{\frac{1}{2}}u{\Vert }^{\beta }Au+g(u^{\prime })=0$ in a finite dimensional Hilbert space under suitable assumptions on $g$.