Asymptotics of the eigenvalues for a boundary value problem with δ-like coefficients

For a spectral problem with delta-like coefficients we develop an asymptotic method for finding minimal eigenvalues and the corresponding eigenfunctions. We prove the obtained asymptotics and estimate the remainder term for large values of the parameter U that specifies the tendency of delta-like coefficients to the delta function. The technique of constructing asymptotic expansions is represented for the case of the spectral problem for the concentration convection in a plane horizontal layer of a fluid with admixture in a transverse force field. However, the proof of the resulting asymptotic expansions is, in a sense, only slightly related to peculiarities of the specific problem and can be used for a broad class of operator equations.