ABSTRACT
This is the second chapter on singular Sturm-Liouville boundary value problems, eigenvalue problems, and their Green's functions. In Chapter 5 the Sturm-Liouville differential equation − ( p ( x ) y ′ ( x ) ) ′ + q ( x ) y ( x ) = f ( x ) , a < x < b https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429437878/305cfe57-5405-49e8-aa24-026d18958f49/content/math6_1.jpg"/> was singular because p ( x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429437878/305cfe57-5405-49e8-aa24-026d18958f49/content/inline-math6_1.jpg"/> could vanish at one endpoint of the interval [ a , b ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429437878/305cfe57-5405-49e8-aa24-026d18958f49/content/inline-math6_2.jpg"/> while q ( x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429437878/305cfe57-5405-49e8-aa24-026d18958f49/content/inline-math6_3.jpg"/> was continuous there. In this chapter, the Strum-Liouville differential equation is singular in two respects. First, p ( x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429437878/305cfe57-5405-49e8-aa24-026d18958f49/content/inline-math6_4.jpg"/> can vanish at one endpoint of the interval [ a , b ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429437878/305cfe57-5405-49e8-aa24-026d18958f49/content/inline-math6_5.jpg"/> , say at x = a. Second, q ( x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429437878/305cfe57-5405-49e8-aa24-026d18958f49/content/inline-math6_6.jpg"/> also is singular at x = a, with a singularity of the form q ( x ) = q 1 ( x ) / ( x − a ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429437878/305cfe57-5405-49e8-aa24-026d18958f49/content/inline-math6_7.jpg"/>
