| Abstract: |
| We consider a one-dimensional superlinear indefinite problem with a piecewise constant weight. Due to the shape of the nonlinearity, this kind of problems can be used to describe the spatial distribution of the steady-states in population genetics models.
We study the number of positive steady-states, which depends on the range of the parameters of the problem. We obtain results on the multiplicity of positive solutions that are sharper than those of previous works in the literature, e.g., P.H. Rabinowitz (Indiana Univ. Math. J., 1973/74), Y. Lou, W.-M. Ni and L. Su (DCDS, 2010), K. Nakashima, W.-M. Ni and L. Su (DCDS, 2010), and G. Feltrin and E. Sovrano (Nonlinearity, 2018).
This is a joint work with G. Feltrin (Univ. Udine, Italy) and E. Sovrano (U. Modena and Reggio Emilia, Italy). |
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