Abstract
Inverse nodal problem consists in constructing operators from the given nodes (zeros) of their eigenfunctions. In this work, the Sturm‐Liouville problem with one classical boundary condition and another nonlocal integral boundary condition is considered. We prove that a dense subset of nodal points uniquely determine the boundary condition parameter and the potential function of the Sturm‐Liouville equation. We also provide a constructive procedure for the solution of the inverse nodal problem.
Highlights
Boundary problems with nonlocal conditions are a part of fast developing differential equations theory
Sturm-Liouville problems with integral conditions constitute a very interesting class of problems since they include as special cases two, three- and multi-point boundary conditions
Nonlocal conditions come up when value of the function on the boundary is connected to values inside the domain
Summary
Boundary problems with nonlocal conditions are a part of fast developing differential equations theory. Some authors have reconstructed the potential function for generalizations of the Sturm-Liouville problem from the nodal points (for example, refer to [3, 5, 7, 8, 10, 12, 15, 16, 17, 18, 22, 27, 28, 29, 31, 34]). We prove the corresponding uniqueness theorem and provide a constructive procedure for the solution
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