An equation in nonlinear combination of iterates
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917565539811328 |
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| author | Gopalakrishna, Chaitanya Zhang, Weinian |
| author_facet | Gopalakrishna, Chaitanya Zhang, Weinian |
| contents | In this paper we deal with an equation in nonlinear combination of iterates. Although it can be reduced by the logarithm conjugacy to a form for application of Schauder's or Banach's fixed point theorems, a difficulty called Zero Problem is encountered for continuous solutions because the domain does not contain $0$. So we consider solutions with weaker regularity, using the Knaster-Tarski fixed point theorem for complete lattices to give order-preserving solutions. Then we give semi-continuous solutions and integrable solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_06420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An equation in nonlinear combination of iterates Gopalakrishna, Chaitanya Zhang, Weinian Dynamical Systems Classical Analysis and ODEs Rings and Algebras 39B12, 47J05, 06F20 In this paper we deal with an equation in nonlinear combination of iterates. Although it can be reduced by the logarithm conjugacy to a form for application of Schauder's or Banach's fixed point theorems, a difficulty called Zero Problem is encountered for continuous solutions because the domain does not contain $0$. So we consider solutions with weaker regularity, using the Knaster-Tarski fixed point theorem for complete lattices to give order-preserving solutions. Then we give semi-continuous solutions and integrable solutions. |
| title | An equation in nonlinear combination of iterates |
| topic | Dynamical Systems Classical Analysis and ODEs Rings and Algebras 39B12, 47J05, 06F20 |
| url | https://arxiv.org/abs/2401.06420 |