id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-852	N. Sasikala	On the Oscillation of a Class of Conformable Schrodinger Equations	2024	11	.pdf	application/pdf	3932	243	71	Evaluate of (2.5) and (2.6) gives �̂� − ∫   Ω(1,𝑟)   𝑟𝛼−𝑛+𝜆𝑝(𝑥)𝑑𝑥 = ∫   𝑆(𝑟)   𝑟𝛼−𝑛+𝜆⟨𝑊, 𝑒𝑖⟩𝑑𝑆 + ∫   Ω(𝑟,∞)   (𝛼 − 𝑛 + 𝜆)𝑟−𝑛+𝜆⟨𝑊, 𝑒𝑖⟩𝑑𝑥 − ∫   Ω(𝑟,∞)   𝑟𝛼−𝑛+𝜆 ∥ 𝑊 ∥2 𝑑𝑥, (2.7) where �̂� = ∫   𝑆(𝑎)   𝑟𝛼−𝑛+𝜆⟨𝑊, 𝑒𝑖⟩𝑑𝑆 + ∫   Ω(𝑎,∞)   (𝛼 − 𝑛 + 𝜆)𝑟−𝑛+𝜆⟨𝑊, 𝑒𝑖⟩𝑑𝑥 + ∫   Ω(1,𝑎)   𝑟𝛼−𝑛+𝜆𝑝(𝑥)𝑑𝑥 − ∫   Ω(𝑎,∞)   𝑟𝛼−𝑛+𝜆 ∥ 𝑊 ∥2 𝑑𝑥, is a finite number. By the Cauchy inequality, 1 𝑅𝛼 ∫   𝑅 𝑎  ∫   𝑠(𝑟)  𝑟𝛼−𝑛+𝜆⟨𝑊, 𝑒𝑖⟩𝑑𝑆𝑑𝛼𝑟 ≤ (𝑇𝛼𝜒(𝑅)) 1 2 ( 𝜔𝑛𝑅𝜆+2𝛼 (𝜆 + 𝛼)(𝜆 + 2𝛼) ) 1 2 1 𝑅𝛼 ∫   𝑅 𝑎  ∫   Ω(𝑎,𝑟)   (𝛼 − 𝑛 + 𝜆)𝑟−𝑛+𝜆⟨𝑊, 𝑒𝑖⟩𝑑𝑥𝑑𝛼𝑟 ≤ (𝛼 − 𝑛 + 𝜆)(𝜒(𝑅)) 1 2 ( 𝜔𝑛𝑅𝜆 𝜆(𝜆 − 𝛼) ) 1 2 .	cache/cana-852.pdf	txt/cana-852.txt