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Keywords = equidiffusive logistic reaction

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13 pages, 286 KiB  
Article
On an Anisotropic Logistic Equation
by Leszek Gasiński and Nikolaos S. Papageorgiou
Mathematics 2024, 12(9), 1280; https://doi.org/10.3390/math12091280 - 24 Apr 2024
Viewed by 885
Abstract
We consider a nonlinear Dirichlet problem driven by the (p(z),q)-Laplacian and with a logistic reaction of the equidiffusive type. Under a nonlinearity condition on a quotient map, we show existence and uniqueness of positive solutions [...] Read more.
We consider a nonlinear Dirichlet problem driven by the (p(z),q)-Laplacian and with a logistic reaction of the equidiffusive type. Under a nonlinearity condition on a quotient map, we show existence and uniqueness of positive solutions and the result is global in parameter λ. If the monotonicity condition on the quotient map is not true, we can no longer guarantee uniqueness, but we can show the existence of a minimal solution uλ* and establish the monotonicity of the map λuλ* and its asymptotic behaviour as the parameter λ decreases to the critical value λ^1(q)>0 (the principal eigenvalue of (Δq,W01,q(Ω))). Full article
(This article belongs to the Special Issue Problems and Methods in Nonlinear Analysis)
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