Existence of almost-periodic ultra-weak solutions to the equation \(u'(t)=a(t)Au(t)+f(t)\) in Hilbert spaces (Q1822676)

Summary: We consider the non-homogeneous first order differential equation: \(du/dt-a(t)Au(t)=f(t)\) in a separable Hilbert space H, under a few assumptions about the complex-valued almost-periodic function a(t) and the linear operator A in H. We establish a sufficient condition, ensuring, for almost-periodic f(t), \({\mathbb{R}}\to H\), the existence (and uniqueness) of an almost-periodic ultra-weak solution of the above equation.