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In this paper we study the boundary value problem for the equation where a,b are real fixed numbers, and a." o<2, (J.j, are nonnegative real numbers such that (o^ + P-)) i°<2 + > Here (3) <£u := -pu" + qu' + ru is the Sturm-Liouville differential expression with p,q,r e C([a,b]) such that p(x)> 0 and r(xi t 0 for all x e [a,b], me C([a,b]) is a given (real-valued) weight function, X e R is the eigenvalue parameter; it is assumed that r(x)> 0 for x e [a,b] if a^ = = The object of this paper isdoi:10.1515/dema-1988-0319 fatcat:rx4xoe7nijd6pe2pe5vtstn6sy