The Distribution of Zeroes and Critical Points of Solutions of a Second Order Half-Linear Differential Equation

Table 4

Comparison of upper bounds for 𝑏 in Example 15.

Exponent 𝑟	Case	Theorem 8	[4, Corollary 2.6]	[4, Theorem 3.1]
𝑟=1.5	𝑦(1)=𝑦^′(𝑏)=0	𝑏≤1.13	𝑏≤1.325	𝑏≤1.33
𝑟=1.5	𝑦^′(1)=𝑦(𝑏)=0	No valid 𝑏	No valid 𝑏	𝑏≤1.33
𝑟=5.0	𝑦(1)=𝑦^′(𝑏)=0	𝑏≤1.28	𝑏≤1.39	𝑏≤1.83
𝑟=5.0	𝑦^′(1)=𝑦(𝑏)=0	𝑏≤1.68	𝑏≤2.19	𝑏≤1.83