• Corpus ID: 211020583

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}
}
  • B. Ricceri
  • Published 4 February 2020
  • Mathematics, Physics
  • arXiv: Analysis of PDEs
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… 
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References

SHOWING 1-10 OF 29 REFERENCES
On the Infimum of Certain Functionals
Here is a particular case of our main result: Let X be a real Banach space, \(\varphi: X \rightarrow \mathbf{R}\) a nonzero continuous linear functional and ψ: X → R a nonconstant Lipschitzian
Applying twice a minimax theorem
Here is one of the results obtained in this paper: Let $X, Y$ be two convex sets each in a real vector space, let $J:X\times Y\to {\bf R}$ be convex and without global minima in $X$ and concave in
A remark on variational inequalities in small balls
In this paper, we prove the following result: Let $(H,\langle\cdot,\cdot\rangle)$ be a real Hilbert space, $B$ a ball in $H$ centered at $0$ and $\Phi:B\to H$ a $C^{1,1}$ function, with $\Phi(0)\neq
Energy functionals of Kirchhoff-type problems having multiple global minima
In this paper, using the theory developed in [8], we obtain some results of a totally new type about a class of non-local problems. Here is a sample: Let $\Omega\subset {\bf R}^n$ be a smooth
A minimax theorem in infinite-dimensional topological vector spaces
In this paper, we obtain a minimax theorem by means of which, in turn, we prove the following result: Let $E$ be an infinite-dimensional reflexive real Banach space, $T:E\to E$ a non-zero compact
Well-posedness of constrained minimization problems via saddle-points
  • B. Ricceri
  • Mathematics, Computer Science
    J. Glob. Optim.
  • 2008
TLDR
A very general well-posedness result is proved for a class of constrained minimization problems of which the following is a particular case: Let X be a Hausdorff topological space and J, Phi: X be two non-constant functions such that J has sequentially compact sub-level sets and admits a unique global minimum in X.
Strongly indefinite functionals and multiple solutions of elliptic systems
We study existence and multiplicity of solutions of the elliptic system \( \left\{{\begin{array}{*{20}l} {- \Updelta u = H_{u} (x,u,v)} \hfill & {{\text{in}}\,\Upomega,} \hfill \\ {- \Updelta v =
A strict minimax inequality criterion and some of its consequences
In this paper, we point out a very flexible scheme within which a strict minimax inequality occurs. We then show the fruitfulness of this approach presenting a series of various consequences. Here is
Sublevel sets and global minima of coercive functionals and local minima of their perturbations
The aim of the present paper is essentially to prove that if $\Phi$ and $\Psi$ are two sequentially weakly lower semicontinuous functionals on a reflexive real Banach space and if $\Psi$ is also
Another multiplicity result for the periodic solutions of certain systems
In this paper, we deal with a problem of the type $$\cases{(\phi(u'))'=\nabla_xF(t,u) & in $[0,T]$\cr & \cr u(0)=u(T)\ , \hskip 3pt u'(0)=u'(T)\ ,\cr}$$ where, in particular, $\phi$ is a
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