The boundary-value problem for differential-operator equations of the first order in a locally convex space
Let \(H\) be a countably complete locally convex space, with topology generated by a multi-norm \(\{\|\cdot\|_p: \enskip p\in{\mathcal{P}}\}\) and let \(A:H\to H\) be a linear continuous operator. The author investigates the problem of finding a solution of equation \[ u'(t)=Au(t) \] satisfying the boundary condition \[ \mu u(a)-u(b)=x_0, \] where \(u:\mathbb{C}\to H\) is a vector-valued function, \(a, b\in \mathbb{C}\), \(a\neq b,\) \(\mu\neq 0\) and \(x_0\) is a point in an appropriate domain depending on the operator \(A\).
linear differential equations in abstract spaces
scientific article; zbMATH DE number 5975440
scientific article