Results 251 to 260 of about 469,372 (283)

A Critical Points Theorem and Nonlinear Differential Problems

Journal of Global Optimization, 2004
Both \textit{D. Averna} and \textit{G. Bonanno} [Topol. Methods Nonlinear Anal. 22, 93--103 (2003; Zbl 1048.58005)], and \textit{G. Bonanno} [Nonlinear Anal., Theory Methods Appl. 54, 651--665 (2003; Zbl 1031.49006)] established a theorem on the existence of 3 critical points of a functional of the type \(\Phi - \lambda J\) for each \(\lambda\) in a ...
openaire   +3 more sources

Existence theorems of multiple critical points and applications

Nonlinear Analysis: Theory, Methods & Applications, 2005
By applying the method of invariant sets of descending flows, the authors discuss the multiplicity of critical points of a functional and obtain a theorem which is called chain of rings theorem. As an application, they utilize this result to lead to the existence of at least seven or nine solutions for nonlinear elliptic boundary value problems.
Sun, Jingxian, Sun, Jinli
openaire   +2 more sources

Critical Point Theorems and Applications to Differential Equations

Acta Mathematica Sinica, 2004
This paper contains a generalization of the Palais-Smale and Cerami conditions. The new compactness condition is first used to obtain a deformation lemma in real Banach spaces. The main abstract result of this paper is a minimax theorem which generalizes the Rabinowitz saddle point theorem and the Benci-Rabinowitz linking theorem.
openaire   +1 more source

Metric critical point theory: Potential Well Theorem and its applications

Rendiconti del Seminario Matematico e Fisico di Milano, 1995
After some necessary definitions of critical and regular points for continuous functions, the authors give a survey of applications of the nonsmooth critical point theory.
Ioffe, Alexander, Schwartzman, Efim
openaire   +2 more sources

A static bifurcation theorem for critical points

Nonlinear Analysis: Theory, Methods & Applications, 1990
In a real Hilbert space \(H\) the problem \(\min_{x\in H} F(x,\lambda)\), where \(\lambda\in\mathbb{R}\), \(F: H\times\mathbb{R}\to \mathbb{R}\) is a \(C^ 2\)-real valued function and \(f(x,\lambda)=d_ xF(x,\lambda)\) is the gradient of \(F\), is considered. It is supposed that a \(C^ 2\)-smooth curve \(x(\lambda)\) of critical points of \(F\) is given.
openaire   +1 more source

Critical types of krasnoselskii fixed point theorems in weak topologies

Quaestiones Mathematicae, 2015
In this note, by means of the technique of measures of weak noncompactness, we establish a generalized form of fixed point theorem for the sum of T + S in weak topology setups of a metrizable locally convex space, where S is not weakly compact, I − T allows to be noninvertible, and T is not necessarily continuous.
Amar, Afif Ben, Xiang, Tian
openaire   +2 more sources

Some remarks on a three critical points theorem

Nonlinear Analysis: Theory, Methods & Applications, 2003
This paper establishes several applications to nonlinear boundary value problems of the three critical points theorem of Ricceri. First, the author proves several abstract results related to a strict minimax inequality. As applications, there are established multiplicity results for nonlinear elliptic problems, including: (i) a two-point boundary value
openaire   +2 more sources

On the relationship between two three-critical-point theorems

Nonlinear Analysis: Theory, Methods & Applications, 2012
This paper deals with two recent results by Ricceri concerning the existence of multiple critical points for certain functionals defined on reflexive real Banach spaces. These abstract results are concerned with the following results: (i) existence of a local minimum and (ii) a minimax inequality together with a coercivity assumption that leads the ...
FARACI, FRANCESCA, MOSCONI, SUNRA JOHANNES NIKOLAJ   +1 more
openaire   +2 more sources

Some Abstract Critical Point Theorems and Applications in Wave Equations

Frontiers of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Jiayang, Wang, Qi, Wu, Li
openaire   +1 more source

Generalizing the Lusternik-Schnirelmann critical point theorem

2019
In this paper, the author obtains the multiplicity of critical points of a continuously differentiable functional $\varphi:\mathcal{V}\times D\longrightarrow\mathbb{R}$, defined on the product of an $N$-dimensional compact manifold $\mathcal{V}$ of class $C^{2}$ without boundary and an $M$-dimensional convex compact set $D$ with nonempty interior ...
openaire   +2 more sources