A Class of Equations with Three Solutions

@article{Ricceri2020ACO,
  title={A Class of Equations with Three Solutions},
  author={Biagio Ricceri},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
  • B. Ricceri
  • Published 29 February 2020
  • Mathematics, Physics
  • arXiv: Analysis of PDEs
Here is one of the results obtained in this paper: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, let $q>1$, with $q \lambda_1$ and for every convex set $S\subseteq L^{\infty}(\Omega)$ dense in $L^2(\Omega)$, there exists $\alpha\in S$ such that the problem $$\cases{-\Delta u=\lambda(u^+-(u^+)^q)+\alpha(x) & in $\Omega$ \cr & \cr u=0 & on $\partial\Omega$\cr}$$ has at least three weak solutions, two of which are global minima in $H^1_0(\Omega)$ of the functional $$u\to {{1}\over {2… 
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Correction: Ricceri, B. A Class of Equations with Three Solutions. Mathematics 2020, 8, 478
The author wishes to make the following correction to this paper [...]
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Italy e-mail address: ricceri@dmi