## Student Work

6-1-1970

Thesis

#### Degree Name

Master of Arts (MA)

Mathematics

#### First Advisor

Dr. Paul A. Haeder

#### Abstract

This study will deal with the zeros of solutions of self-adjoint linear differential equations of second order. In the following we consider some def1n1t1ons and theorems that relate to ordinary differential equations. Definition 1.1. A homogeneous linear differential equation of order n has the form a0y{n ) + a1y(n-l) + ••• +any= 0 where a0 �� 0 and e��ch a1 = a 1(x) is continuous on an interval (a,b), 1 = 1,2, ••• ,n. Definition 1.2. If L(y) 1s a linear operator and L(y) = a0(x)y''(x) + a1(x)y'(x) + a2 (x)y(x}, then 1ts adjoint, L(z}, 1s denoted by [��0(x)z(x)] '' - [a1 (x)z(x)]' + a2(x)z(x). If L(y) = L(y), then the differential equation, L(y): 0 is self-adjoint of second order. number of theorems, some of them included without proof, were used as a basis for the study 1n this thesis. Theorem 1.1. L(y) = 0 is self-adjoint 1f and only if a1(x) = a0•(x). (5, p. 98)

#### Comments

A Thesis Presented to the Department of Mathematics and the Faculty of the Graduate College University of Nebraska at Omaha In Partial Fulfillment of the Requirements for the Degree Master of Arts Copyright 1970 Marsha J. Hunter

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