Abstract For a quadratic Markov branching process (QMBP), we show that the decay parameter is equal to first eigenvalue of Sturm–Liouville operator associated with partial differential equation generating function transition probability satisfies. The proof based on spectral properties operator. Both upper and lower bounds are given explicitly by means version Hardy’s inequality. Two examples p...

In this paper, we consider the negative order Korteweg–de Vries equation with a self-consistent integral source. It is shown that negative-order source can be integrated by method of inverse spectral problem. The evolution data Sturm–Liouville operator periodic potential associated solution determined. obtained results make it possible to apply problem solve in class functions.