Existence Results and Strong Maximum Principle for a Resonant Sublinear Elliptic Problem
Keywords:
Sublinear elliptic problem, resonance, nonnegative solution, positive solution, mini max method, mountain pass, strong maximum principle.Abstract
Let Ω be a bounded smooth connected open set in RN and let λ1 be the first eigenvalue of the Laplacian on Ω. We study the resonant elliptic problem −∆u=λ1u+us−1−µur−1, u ≥0, u|∂Ω = 0 in Ω in Ω where s ∈]1,2[, r ∈]1,s[, and µ ∈]0,+∞[. An existence result of nonzero solutions is established via minimax and perturbation methods. Furthermore, for µ large enough, we prove a Strong Maximum Principle for the solutions of this problem. In particular, we extend to higher dimension an analogous recent result obtained in the one-dimensional case via the time-mapping method
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