Eigenschaften der algebraisch-logarithmischen Integrale linearer nicht homogener Differentialgleichungen.
For any complex valued L p-function b(x), 2 ≤ p < ∞, or L ∞-function with the norm ‖b↾L ∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d 2/dx 2 + x 2 + b(x) in L 2(ℝ1) is discrete and eventually simple. Its SEAF (system of eigen- and associated functions) is an unconditional basis in L 2(ℝ).
The paper is concentrated on Professor Miloš Ráb and his contribution to the theory of oscillatory properties of solutions of second and third order linear differential equations, the theory of differential equations with complex coefficients and dynamical systems, and the theory of nonlinear second order differential equations. At the beginning, we take a brief look at the most important moments in his life. Afterwards, we describe his scientific activities on mentioned theories.