Loop type subcontinua of positive solutions for indefinite concave-convex problems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2017
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910301340827648 |
|---|---|
| author | Kaufmann, Uriel Quoirin, Humberto Ramos Umezu, Kenichiro |
| author_facet | Kaufmann, Uriel Quoirin, Humberto Ramos Umezu, Kenichiro |
| contents | We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights, under Dirichlet and Neumann boundary conditions. Our approach depends on local and global bifurcation analysis from the zero solution in a non-regular setting, since the nonlinearities considered are not differentiable at zero, so that the standard bifurcation theory does not apply. To overcome this difficulty, we combine a regularization scheme with a priori bounds, and Whyburn's topological method. Furthermore, via a continuity argument we prove a positivity property for subcontinua of nonnegative solutions. These results are based on a positivity theorem for the associated concave problem proved in [15], and extend previous results established in the powerlike case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_07802 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Loop type subcontinua of positive solutions for indefinite concave-convex problems Kaufmann, Uriel Quoirin, Humberto Ramos Umezu, Kenichiro Analysis of PDEs We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights, under Dirichlet and Neumann boundary conditions. Our approach depends on local and global bifurcation analysis from the zero solution in a non-regular setting, since the nonlinearities considered are not differentiable at zero, so that the standard bifurcation theory does not apply. To overcome this difficulty, we combine a regularization scheme with a priori bounds, and Whyburn's topological method. Furthermore, via a continuity argument we prove a positivity property for subcontinua of nonnegative solutions. These results are based on a positivity theorem for the associated concave problem proved in [15], and extend previous results established in the powerlike case. |
| title | Loop type subcontinua of positive solutions for indefinite concave-convex problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1710.07802 |