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Asymptotic integration of the second order differential equation, resonance effect

In: Tatra Mountains Mathematical Publications, vol. 63, no. 2
Barbara Pietruczuk
Detaily:
Rok, strany: 2015, 223 - 235
Kľúčové slová:
resonance, Wigner--von Neumann potential, asymptotic behaviour
O článku:
There will be presented asymptotic formulas for solutions of the equation \begin{equation*}y''+\bl(1 +\varphi(x)\br)y=0,\qquad >x_0>x>\infty,\end{equation*} 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.
Ako citovať:
ISO 690:
Pietruczuk, B. 2015. Asymptotic integration of the second order differential equation, resonance effect. In Tatra Mountains Mathematical Publications, vol. 63, no.2, pp. 223-235. 1210-3195.

APA:
Pietruczuk, B. (2015). Asymptotic integration of the second order differential equation, resonance effect. Tatra Mountains Mathematical Publications, 63(2), 223-235. 1210-3195.