Left-Definite Boundary Conditions of Regular Fourth-Order Differential Operators
GAO Yunlan1, PENG Tao2, SUN Jiong3
1. College of Science, Inner Mongolia University of Technology, Hohhot 010051;2. Shangdong Zibo Building Schools, Zibo 256400;3. College of Science and Technology, Inner Mongolia University, Hohhot 010021
In this paper, we discuss the left-definite boundary conditions of a class of fourth-order differential operators, and we study the left-definite problems by the positive definiteness of the self-adjoint extension. Besides, we give the necessary and sufficient conditions of left-defined problem by means of the cofficient of self-adjoint differential operators, the endpoints of interval and boundary conditions. Moreover, we correspondingly obtain all of the left-defined boundary matrix of fourth-order self-adjoint differential operators.