On recovering quadratic pencils with singular coefficients and entire functions in the boundary conditions

The paper deals with a new type of inverse spectral problems for second-order quadratic differential pencils when one the boundary conditions involves arbitrary entire functions parameter. Although various aspects theory have been special interest during last decades, such settings were considered before only in particular case Sturm–Liouville equation. We develop an approach covering also dependence on parameter equation, which is based completeness and basisness certain functional systems. By this approach, we obtain uniqueness theorem algorithm solving problem along sufficient properties mentioned presented results give universal tool studying number important specific situations, including Hochstadt–Lieberman-type both interval geometrical graphs, illustrated as well.