Weak singularities may help periodic solutions to exist (Q859526)
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scientific article; zbMATH DE number 5116272
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak singularities may help periodic solutions to exist |
scientific article; zbMATH DE number 5116272 |
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Weak singularities may help periodic solutions to exist (English)
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16 January 2007
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There are given conditions for the existence of a positive T-periodic solution of the equation \[ x''+ a(t)x= f(t,x)+ c(t), \] under the assumption, that the equation \[ x''+ a(t)x= 0 \] is nonresonant, that the corresponding Green's function is nonnegative and \[ 0\leq f(x,t)\leq b(t)/x^\lambda,\qquad 0<\lambda< 1. \]
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periodic solution
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weak singularity
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Schauder's fixed point theorem
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