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

question 14

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) \(p\) , \(q\) , \(r\) piecewise 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) \(A _ { 1 } B _ { 1 } \neq 0\)
• E) \(A _ { 1 } ^ { 2 } + B _ { 1 } ^ { 2 } \neq 0\)

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