Beck’s Problem

Source abstract

Beck’s problem is concerned with the stability of the zero solution of a linear nonconservative boundary value problem depending on a parameter p. The minimum positive value of p for which the zero solution becomes unstable is known as the critical value. The analysis of the first two eigenvalues of a certain operator shows that $p^ * \sim 20.05$ is an upper bound for the critical value. In this paper we prove that the critical value is $p^ *$.