Year: 2025
Type: preprint
Abstract: We investigate nonnegative solutions of indefinite elliptic problems which enjoy the dead core phenomenon. Our model is the subhomogeneous problem $$ -Δ_p u = (a^+(x) - μa^-(x))|u|^{q-2}u, \quad u \in W_0^{1,p}(Ω), $$ where $Ω$ is a bounded domain in $\mathbb{R}^N$, $1 0$. Thanks to a dead core formation property, we obtain multiple nonnegative dead core solutions of this problem for $μ$ large enough. This assertion, in combination with a uniqueness feature, yields an exact multiplicity result, which gives a precise description of the nonnegative solutions set of this problem for large values of $μ$. We also extend the multiplicity result to other classes of problems.
Source: arXiv (Cornell University)
Authors: Bobkov, Vladimir, Quoirin, Humberto Ramos
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416834973
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