Resumen de Separation for ordinary differential equation with matrix coeficient
B. A. El-Gendi, A. S. Mohamed
In this paper we give criteria for the separation of the differential operator $$L[u] = (-1)^mD^{2m}u(x) + q(x)u(x)$$ in the space $L_p(\mathbb{R})^\ell,\ell , m\in N$ and $p\in (1,\infty)$ where $q(x), x\in R$, is a $\ell\times\ell$ positive hermitian matrix and prove the existence and uniqueness of the solution for the differential equation $$(L + \beta E)u(x) = f(x), f(x)\in L_p(\mathbb{R})^\ell$$ where $E$ is the identity operator and $\beta\geq 1$.
