Solution of the inverse problem for Bessel operator on an interval [Formula: see text]

Area of Science:

• Differential Equations
• Mathematical Physics
• Harmonic Analysis

Background:

• The study addresses the inverse nodal problem, a key area in spectral analysis.
• Bessel-type p-Laplacian problems present unique challenges due to their non-linear nature.
• Classical Sturm-Liouville theory provides a foundation but requires adaptation for p-Laplacian equations.

Purpose of the Study:

• To solve the inverse nodal problem for a specific Bessel-type p-Laplacian equation.
• To determine nodal parameters, including nodal points and lengths.
• To reconstruct the potential function from the obtained nodal data.

Main Methods:

• The study employs techniques for solving inverse spectral problems.
• Nodal points and lengths are derived from the solution of the p-Laplacian equation.
• Reconstruction of the potential function is achieved using the calculated nodal parameters.

Main Results:

• Nodal parameters (points and lengths) for the Bessel-type p-Laplacian problem were successfully obtained.
• The potential function was reconstructed accurately using the nodal points.
• The results demonstrate a similarity to classical Sturm-Liouville problem solutions, with novel insights.

Conclusions:

• The inverse nodal problem for the specified Bessel-type p-Laplacian equation is solvable.
• The method allows for the reconstruction of the potential function from spectral data.
• This work extends spectral theory to a class of non-linear differential equations with specific boundary conditions.