Bifurcation and multiplicity results for elliptic problems with subcritical nonlinearity on the boundary
We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use rescaling method, degree theory and continuation theorem to prove that there exists a connected branch of posit...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/7250 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/7250 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.9 Elliptic problem Nonlinear boundary conditions Superlinear and subcritical Local bifurcation Degree theory Global bifurcation. Análisis matemático Ecuaciones diferenciales 1202 Análisis y Análisis Funcional 1202.07 Ecuaciones en Diferencias |
| Sumario: | We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use rescaling method, degree theory and continuation theorem to prove that there exists a connected branch of positive solutions bifurcating from infinity when the parameter goes to zero. Moreover, if the nonlinearity satisfies additional conditions near zero, we establish a global bifurcation result, and discuss the number of positive solution(s) with respect to the parameter using bifurcation theory and degree theory. |
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