Let Omega be a bounded smooth connected open set in R-N and let lambda(1) be the first eigenvalue of the Laplacian on Omega. We study the resonant elliptic problem-Delta u = lambda(1)u + u(s-1) - mu u(r-1), in Omega u >= 0, in Omega u(vertical bar partial derivative Omega) = 0where s is an element of]1, 2[, r is an element of]1, s[, and mu is an element of]0,+infinity[. An existence result of nonzero solutions is established via minimax and perturbation methods. Furthermore, for mu 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.
Existence Results and Strong Maximum Principle for a Resonant Sublinear Elliptic Problem
Anello, G
2019-01-01
Abstract
Let Omega be a bounded smooth connected open set in R-N and let lambda(1) be the first eigenvalue of the Laplacian on Omega. We study the resonant elliptic problem-Delta u = lambda(1)u + u(s-1) - mu u(r-1), in Omega u >= 0, in Omega u(vertical bar partial derivative Omega) = 0where s is an element of]1, 2[, r is an element of]1, s[, and mu is an element of]0,+infinity[. An existence result of nonzero solutions is established via minimax and perturbation methods. Furthermore, for mu 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.Pubblicazioni consigliate
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