The effects of indefinite nonlinear boundary conditions on the structure of the positive solutions set of a logistic equation |
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Authors: | Humberto Ramos Quoirin Kenichiro Umezu |
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Institution: | 1. Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile;2. Department of Mathematics, Faculty of Education, Ibaraki University, Mito 310-8512, Japan |
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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. |
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Keywords: | 35J25 35J61 35B32 35P30 |
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