@article{Jleli2025, 
author = {Mohamed Jleli and Bessem Samet},
title = {Lyapunov-type inequalities for self-adjoint differential equations of second order},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {21675-21692},
keywords = {self-adjoint differential equations, Lyapunov-type inequalities, generalized radial Schrödinger's equation, modified Bessel's differential equation},
url = {https://www.sciopen.com/article/10.3934/math.2025963},
doi = {10.3934/math.2025963},
abstract = {We present a general method that yields Patula, Hartman-Wintner, and Lyapunov-type inequalities for the second-order differential equation     −  (  α  (  x  )      u    ′    (  x  )      )    ′    +  β  (  x  )  u  (  x  )  =  γ  (  x  )  u  (  x  )  ,    x  ∈  I  ,where    I is an interval of        R  ,    α  ∈      C    1    (  I  ),    α  >  0,    β  ,  γ  ∈  C  (  I  ), and    β  ≥  0. Applications cover the generalized radial Schrödinger equation and the modified Bessel equation and include an improved (sharpened) form of Bargmann's inequality.}
}