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In this talk, we consider the positive solutions of the logistic elliptic equation having a nonlinear boundary condition with an indefinite weight, according to a parameter, and investigate the role played by the weight in determining the structure of the positive solution set. Using variational and bifurcation techniques, we prove the existence of at least three positive solutions in some range of the parameter and the asymptotic behavior. Eventually, we discuss the existence of a CS-shaped as well as an S-shaped bifurcation diagrams. This is a joint work with Humberto Ramos Quoirin. |
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