The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions

Table 4

Comparison of bounds for 𝑏 in Example 4.

Value of 𝐴	Used formula	Bound
𝐴=3	∫^𝑏𝑎𝑞(𝑡)𝐺(𝑡,𝑡)𝐿^11{1}(𝑡)𝑑𝑡>1	𝑏>1.266
	Theorem 12 with 𝑘=11	𝑏>1.279
	𝐿^5{𝑣}^22<‖𝑣‖^22	𝑏<1.287
	𝐿^10{𝑣}𝑎+𝑏2<1	𝑏<1.298
𝐴=5	∫^𝑏𝑎𝑞(𝑡)𝐺(𝑡,𝑡)𝐿^11{1}(𝑡)𝑑𝑡>1	𝑏>1.044
	Theorem 12 with 𝑘=11	𝑏>1.056
	𝐿^5{𝑣}^22<‖𝑣‖^22	𝑏<1.062
	𝐿^10{𝑣}𝑎+𝑏2<1	𝑏<1.071