Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610384 | Journal of Differential Equations | 2014 | 43 Pages |
Abstract
We investigate a semilinear elliptic equation with a logistic nonlinearity and an indefinite nonlinear boundary condition, both depending on a parameter λ. Overall, we analyze the effect of the indefinite nonlinear boundary condition on the structure of the positive solutions set. Based on variational and bifurcation techniques, our main results establish the existence of three nontrivial non-negative solutions for some values of λ, as well as their asymptotic behavior. These results suggest that the positive solutions set contains an S-shaped component in some case, as well as a combination of a C-shaped and an S-shaped components in another case.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Humberto Ramos Quoirin, Kenichiro Umezu,