The Problem Is a Regular Sturm-Liouville Problem Under Certain Conditions, Including Select

question 23

Multiple Choice

The problem $\frac { d } { d x } \left[ r ( x ) y ^ { \prime } \right] + ( q ( x ) + \lambda p ( x ) ) y = 0 , A _ { 1 } y ( a ) + B _ { 1 } y ^ { \prime } ( a ) = 0 , A _ { 2 } y ( b ) + B _ { 2 } y ^ { \prime } ( b ) = 0$ is a regular Sturm-Liouville problem under certain conditions, including Select all that apply.

• A) \(p\) , \(q\) , \(r\) are continuous on \([ a , b ]\)
• B) \(r ( x ) > 0\) and \(p ( x ) < 0\) on \([ a , b ]\)
• C) \(r ( x ) < 0\) and \(p ( x ) > 0\) on \([ a , b ]\)
• D) \(A _ { 1 } ^ { 2 } + B _ { 1 } ^ { 2 } \neq 0\)
• E) \(A _ { 1 } A _ { 2 } \neq 0\)

---

Definitions:

Diverse Stock Portfolio

An investment strategy that involves holding a variety of different stocks to reduce risk.

Small Investors

Small investors refer to individual or retail investors who invest smaller amounts of money in securities, often lacking the market influence of larger institutional investors.

Equity Investments

Financial assets in companies or properties, representing ownership interest and the potential for dividends or capital gains.

Mutual Fund

An investment vehicle made up of a pool of funds collected from many investors for the purpose of investing in securities such as stocks, bonds, and other assets.