On comparison principles for the periodic Hill's equation (Q2909052)
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scientific article; zbMATH DE number 6073819
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On comparison principles for the periodic Hill's equation |
scientific article; zbMATH DE number 6073819 |
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On comparison principles for the periodic Hill's equation (English)
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29 August 2012
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periodic Hill's equation
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Green function
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comparison principle
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0.89982873
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0.88468623
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0.8833846
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0.8825777
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The authors first study the properties of the Green function related to the periodic boundary value problem NEWLINE\[NEWLINEL_a x \equiv x'' +a(t) \, x=0, \quad x(0)=x(T), \, x'(0)=x'(T),NEWLINE\]NEWLINE with a sign-changing potential \(a(t)\). Then, they obtain new explicit criteria to ensure that the maximum or anti-maximum principle holds for this equation. Several illustrative examples show that the obtained criteria complement some previous results in the literature.
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