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arXiv · 1911.03152

Asymptotic behavior of minimal solutions of $-\Delta u=\lambda f(u)$ as $\lambda\to-\infty$

Luca Battaglia·Francesca Gladiali·Massimo Grossi
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Abstract

We consider the Dirichlet problem $-\Delta u=\lambda f(u)$ with $\lambda<0$ and $f$ non-negative and non-decreasing. We show existence and uniqueness of solutions $u_\lambda$ for any $\lambda$ and discuss their asymptotic behavior as $\lambda\to-\infty$. In the expansion of $u_\lambda$ large solutions naturally appear.

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Luca Battaglia, Francesca Gladiali, Massimo Grossi. 2019-11-08. Asymptotic behavior of minimal solutions of $-\Delta u=\lambda f(u)$ as $\lambda\to-\infty$. https://arxiv.org/abs/1911.03152

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