Distribution of Spectrum of the Weber Operator Perturbedby the Dirac Delta Function

We study the Sturm–Liouville operator generated in the Hilbert space $$L^2[0,+\infty ) $$ by a differential expression containing the Dirac delta function with zero boundary condition. We prove that the eigenvalues $$\lambda _n $$ of this operator satisfy certain inequalities. The problem on the location of the first eigenvalue $$\lambda _1$$ depending on the parameters of the differential expression is solved. In particular, we obtain conditions under which $$ \lambda _1$$ is negative.