On the convergence to zero of solutions of a second-order differential equation with complex-valued potential (Q690521)
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scientific article; zbMATH DE number 6110727
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the convergence to zero of solutions of a second-order differential equation with complex-valued potential |
scientific article; zbMATH DE number 6110727 |
Statements
On the convergence to zero of solutions of a second-order differential equation with complex-valued potential (English)
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28 November 2012
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The authors consider the second-order linear differential equation \[ {y}''(t) + A(t)y = 0, \] where \(A:[0,\infty ) \to\mathbb C\) is a differentiable function. They obtain certain sufficient conditions for the potential function assuring that all solutions of the equation converge to zero at infinity and show that the conditions imposed on the potential function are close to the necessary ones.
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differential equation
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solution tending to zero
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monotone function
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Dirichlet criterion
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WKB-estimates
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