Asymptotics of eigenvalues and equiconvergence theorems for operators with power singularities in the boundary conditions. (Russian) Zbl 0574.42021
The paper deals with asymptotics of eigenvalues and equiconvergence theorems connected with the operator d/dt considered with integral ”boundary value condition” \(\int^{a}_{-a}y(t)k(t)/(a-| t|)^{\alpha}dt=0,\) \(0<\alpha <1\), \(k\in BV[-a,a]\), \(k(a- 0),k(a+0)\neq 0\) and for the operator \(d^ n/dt^ n\) considered with ”boundary value conditions” including fractional derivatives: \(U_{\nu}(y)=\alpha_{\nu}(-1)^{p_{\nu}}D^{k_{\nu}}y(- a)+\beta_{\nu}D^{k_{\nu}}y(a)=0,\) \(\nu =1,...,n\), \(n-1\geq k_ 1\geq...\geq k_ n>-1\), \(k_{\nu +2}<k_{\nu}\), \(-1\leq p_{\nu}- 1<k_{\nu}\leq p_{\nu}\leq n-1\) where \(p_{\nu}\) are integers.
Reviewer: N.Bozhinov