Uniqueness for degenerate elliptic sublinear problems in the absence of dead cores
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In this work we study the problem
-div (|∇u|p-2 ∇u) = λƒ(u)
in the unit ball of ℝN, with u = 0 on the boundary, where p > 2, and λ is a real parameter. We assume that the nonlinearity ƒ has a zero ū0 > 0 of order k ≥ p-1. Our main contribution is showing that there exists a unique positive solution of this problem for large enough λ and maximum close to ū0. This will be achieved by means of a linearization technique, and we also prove the new result that the inverse of the p-Laplacian is differentiable around positive solutions.
CitationGarcía-Melián, J. (2004). Uniqueness for degenerate elliptic sublinear problems in the absence of dead cores. Electronic Journal of Differential Equations, 2004(110), pp. 1-16.
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