NODES OF EIGENFUNCTIONS OF STURM-LIOIJVILLE PROBLEM WITH AN INDEFINITE WEIGHT FUNCTION

Jan Bochenek
1988 Demonstratio Mathematica  
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 is
more » ... of this paper is to study some properties of eigenvalues and eigenfunctions corresponding to equation (1) and the conditions (2) (we shall also shortly say: eigenvalues and eigenfunctions of problem (1), (2)). From the above assumptions it follows that, if the weight function m is positive in [a,b], then the problem (1), (2) has a smallest eigenvalue A > o. It is the only eigenvalue of (1), (2) corresponding to a positive eigenfunction. -777
doi:10.1515/dema-1988-0319 fatcat:rx4xoe7nijd6pe2pe5vtstn6sy