Abstract:In this paper, we consider the Laplace equation with a class of indefinite superlinear boundary conditions and study the uniqueness of positive solutions that this problem possesses. Superlinear elliptic problems can be expected to have multiple positive solutions under certain situations. To our end, by conducting spectral analysis for the linearized eigenvalue problem at an unstable positive solution, we find sufficient conditions for ensuring that the implicit function theorem is applicable to the unstable … Show more
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