On the simpleness of zeros of Stokes multipliers

Abstract

The aim of this paper is to discuss the simpleness of zeros of Stokes multipliers associated with the differential equation $-{\Phi }^{\prime \prime }(X)+W(X)\Phi (X)=0$, where $W(X)=X^m+a_1{X}^{m-1}+...+a_m$ is a real monic polynomial. We show that, under a suitable hypothesis on the coefficients $a_k$, all the zeros of the Stokes multipliers are simple.