SPECTRAL EXPANSION OF STURM-LIOUVILLE PROBLEMS WITH EIGENVALUE-DEPENDENT BOUNDARY CONDITIONS

Abstract

Abstract. In this paper, we consider the operator L generated in L2(R+) bythe di§erential expressionl(y) = y00 + q(x)y; x2R+ := [0; 1)and the boundary conditiony0(0)y(0)= 0 + 1 + 22;where q is a complex valued function and i 2 C; i = 0; 1; 2 with 2 6= 0. Wehave proved that spectral expansion of L in terms of the principal functionsunder the conditionq 2 AC(R+); limx!1q(x) = 0; supx2R+[e"pxjq0(x)j] 0taking into account the spectral singularities. We have also proved the convergence of the spectral expansion.