Sturm-Liouville theory In mathematics and its applications, a classical Sturm-Liouville equation, named after Jacques Charles François Sturm (1803-1855) and Joseph Liouville (1809-1882), is a real second-order linear differential equation of the form
Amer. Mathematical Society
Mathematical surveys and monographs; v.121
Sturm and Liouville published a series of papers on second order linear ordinary differential equations ordinary differential equation
Equation containing derivatives of a function of a single variable. Its order is the order of the highest derivative it contains (e.g., a first-order differential equation involves only the first derivative of the function). including boundary value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions. back in 1836-37, but the topic is still an area of intense activity today. This monograph is presented with the twin goals of providing a modern survey of the basic properties of the Sturm- Liouville equation and to introduce some aspects of recent research on Sturm-Liouville problems. Chapters cover first order systems, scalar scalar, quantity or number possessing only sign and magnitude, e.g., the real numbers (see number), in contrast to vectors and tensors; scalars obey the rules of elementary algebra. Many physical quantities have scalar values, e.g. initial value problems, two-point regular boundary value problems, regular self-adjoint problems, regular left-definite and indefinite problems, oscillation Oscillation
Any effect that varies in a back-and-forth or reciprocating manner. Examples of oscillation include the variations of pressure in a sound wave and the fluctuations in a mathematical function whose value repeatedly alternates above and below some , the limit-point/limit-circle dichotomy, singular initial value problem, two-point singular boundary value problems, singular self-adjoint problems, singular indefinite problems, singular left-definite problems, and examples.
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