There will be presented asymptotic formulas for solutions of the equation$$y^'' + ( 1 + \varphi (x) ) y = 0, 0 < x_0 < x < \infty ,$$where function $\varphi$ is small in a certain sense for large values of the argument. Usage of method of L-diagonal systems allows to obtain various forms of solutions depending on the properties of function $\varphi$.The main aim will be discussion about the second order differential equations possesing a resonance effect known for Wigner-von Neumann potential. A class of potentials generalizing that of Wigner-von Neumann will be presented.
@article{321,
title = {Asymptotic integration of the second order differential equation, resonance effect},
journal = {Tatra Mountains Mathematical Publications},
volume = {62},
year = {2015},
doi = {10.2478/tatra.v63i0.321},
language = {EN},
url = {http://dml.mathdoc.fr/item/321}
}
Pietruczuk, Barbara. Asymptotic integration of the second order differential equation, resonance effect. Tatra Mountains Mathematical Publications, Tome 62 (2015) . doi : 10.2478/tatra.v63i0.321. http://gdmltest.u-ga.fr/item/321/