# An alternative theorem for gradient systems.

@article{Ricceri2020AnAT, title={An alternative theorem for gradient systems.}, author={Biagio Ricceri}, journal={arXiv: Analysis of PDEs}, year={2020} }

Here is one of the result obtained in this paper: Let $\Omega\subset {\bf R}^2$ be a smooth bounded domain and let $F, G : {\bf R}\to {\bf R}$ be two $C^1$ functions satisfying the following conditions: $(i)$ for some $p>0$, one has $$\limsup_{|\xi|\to +\infty}{{|F'(\xi)|+|G'(\xi)|}\over {|\xi|^p}}<+\infty\ ;$$ $(ii)$ $F$ is non-negative, non-decreasing, $\lim_{\xi\to +\infty}{{F(\xi)}\over {\xi^2}}=0$, $\lim_{\xi\to 0^+}{{F(\xi)}\over {\xi^2}}=+\infty$ and the function $\xi\to {{F'(\xi)}\over…

## 3 Citations

A class of functionals possessing multiple global minima

- Physics, Mathematics
- 2020

We get a new multiplicity result for gradient systems. Here is a very particular corollary: Let $\Omega\subset {\bf R}^n$ ($n\geq 2$) be a smooth bounded domain and let $\Phi:{\bf R}^2\to {\bf R}$ be…

A more complete version of a minimax theorem

- Mathematics
- 2021

In this paper, we present a more complete version of the minimax theorem established in [7]. As a consequence, we get, for instance, the following result: Let X be a compact, not singleton subset of…

A Class of Equations with Three Solutions

- Mathematics, Physics
- 2020

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 $S\subseteq L^{\infty}(\Omega)$…

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