A Dirichlet problem on the half-line for nonlinear equations with indefinite weight
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2015
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| _version_ | 1866916693887942656 |
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| author | Došlá, Zuzana Marini, Mauro Matucci, Serena |
| author_facet | Došlá, Zuzana Marini, Mauro Matucci, Serena |
| contents | We study the existence of positive solutions on the half-line $[0,\infty)$ for the nonlinear second order differential equation \[ \bigl(a(t)x^{\prime}\bigr)^{\prime}+b(t)F(x)=0,\quad t\geq0, \] satisfying Dirichlet type conditions, say $x(0)=0$, $\lim_{t\rightarrow\infty}x(t)=0$. The function $b$ is allowed to change sign and the nonlinearity $F$ is assumed to be asymptotically linear in a neighborhood of zero and infinity. Our results cover also the cases in which $b$ is a periodic function for large $t$ or it is unbounded from below. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1507_06095 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | A Dirichlet problem on the half-line for nonlinear equations with indefinite weight Došlá, Zuzana Marini, Mauro Matucci, Serena Classical Analysis and ODEs 34B40, 34B18 We study the existence of positive solutions on the half-line $[0,\infty)$ for the nonlinear second order differential equation \[ \bigl(a(t)x^{\prime}\bigr)^{\prime}+b(t)F(x)=0,\quad t\geq0, \] satisfying Dirichlet type conditions, say $x(0)=0$, $\lim_{t\rightarrow\infty}x(t)=0$. The function $b$ is allowed to change sign and the nonlinearity $F$ is assumed to be asymptotically linear in a neighborhood of zero and infinity. Our results cover also the cases in which $b$ is a periodic function for large $t$ or it is unbounded from below. |
| title | A Dirichlet problem on the half-line for nonlinear equations with indefinite weight |
| topic | Classical Analysis and ODEs 34B40, 34B18 |
| url | https://arxiv.org/abs/1507.06095 |