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

Luca Battaglia; Francesca Gladiali; Massimo Grossi

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

Analysis of PDEs 2020-06-25 v2

Authors: Luca Battaglia , Francesca Gladiali , Massimo Grossi

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.

Keywords

dirichlet problem semilinear elliptic equation minimal solution asymptotic behavior large solutions

Cite

@article{arxiv.1911.03152,
  title  = {Asymptotic behavior of minimal solutions of $-\Delta u=\lambda f(u)$ as $\lambda\to-\infty$},
  author = {Luca Battaglia and Francesca Gladiali and Massimo Grossi},
  journal= {arXiv preprint arXiv:1911.03152},
  year   = {2020}
}

Comments

18 pages

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