Homoclinic Solution to Zero of a Non-autonomous, Nonlinear, Second Order Differential Equation with Quadratic Growth on the Derivative
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909215881166848 |
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| author | Junior, Pablo dos Santos Corrêa Faria, Luiz Fernando de Oliveira |
| author_facet | Junior, Pablo dos Santos Corrêa Faria, Luiz Fernando de Oliveira |
| contents | This work aims to obtain a positive, smooth, even, and homoclinic to zero (i.e zero at infinity) solution to a non-autonomous, second-order, nonlinear differential equation involving quadratic growth on the derivative. We apply Galerkin's method combined with Strauss' approximation on the term involving the first derivative to obtain weak solutions. We also study the regularity of the solutions and the dependence on their existence with a parameter |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homoclinic Solution to Zero of a Non-autonomous, Nonlinear, Second Order Differential Equation with Quadratic Growth on the Derivative Junior, Pablo dos Santos Corrêa Faria, Luiz Fernando de Oliveira Classical Analysis and ODEs Mathematical Physics Analysis of PDEs 34A34, 34C37, 34D10, 34K12, 34L30 This work aims to obtain a positive, smooth, even, and homoclinic to zero (i.e zero at infinity) solution to a non-autonomous, second-order, nonlinear differential equation involving quadratic growth on the derivative. We apply Galerkin's method combined with Strauss' approximation on the term involving the first derivative to obtain weak solutions. We also study the regularity of the solutions and the dependence on their existence with a parameter |
| title | Homoclinic Solution to Zero of a Non-autonomous, Nonlinear, Second Order Differential Equation with Quadratic Growth on the Derivative |
| topic | Classical Analysis and ODEs Mathematical Physics Analysis of PDEs 34A34, 34C37, 34D10, 34K12, 34L30 |
| url | https://arxiv.org/abs/2406.01772 |