Solution of the inverse problem for Bessel operator on an interval [1,a] $[ 1,a ]$

Abstract

Abstract In this note, we solve the inverse nodal problem for Bessel-type p-Laplacian problem −(y′(p−1))′=(p−1)(λ−ω(x))y(p−1),1≤x≤a,y(1)=y(a)=0, $$\begin{aligned}& - \bigl( y^{{\prime} (p-1)} \bigr) ^{\prime} = ( p-1 ) \bigl( \lambda- \omega(x) \bigr) y^{(p-1)},\quad1\leq x\leq a, \\& y(1) =y(a)=0, \end{aligned}$$ on a special interval. We obtain some nodal parameters like nodal points and nodal lengths. In addition, we reconstruct the potential function by nodal points. Results obtained in this paper are similar to the classical Sturm–Liouville problem. However, equations of this type are considered with the condition defined at the origin. We solve the problem on the interval [1,a] $[1,a]$, that problem is not singular.

Keywords

• Inverse nodal problem
• Prüfer substitution
• Bessel equation