Some problems of spectral theory of fourth-order differential operators with regular boundary conditions

Abstract

In this paper, we consider the problem yIV+q(x)y=λy,0<x<1,y″′(1)-(-1)σy″′(0)+αy′(0)+γy(0)=0,y″(1)-(-1)σy″(0)+βy(0)=0,y′(1)-(-1)σy′(0)=0,y(1)-(-1)σy(0)=0where λ is a spectral parameter; q(x) ∈ L1(0 , 1) is a complex-valued function; α, β, γ are arbit