Related papers: On the Palais principle for non-smooth functionals

We obtain nontrivial solutions of a critical $(p,q)$-Laplacian problem in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical Sobolev exponents, this problem lacks a…

We study the global invertibility of non-smooth, locally Lipschitz maps between infinite-dimensional Banach spaces, using a kind of Palais-Smale condition. To this end, we consider the Chang version of the weighted Palais-Smale condition…

In this paper, we study a class of Banach spaces, called \phi-spaces. In a natural way, we associate a measure of weak compactness in such spaces and prove an analogue of Sadovskii fixed point theorem for weakly sequentially continuous…

We extend Lie's classical method for finding group invariant solutions to the case of non-transverse group actions. For this extension of Lie's method we identify a local obstruction to the principle of symmetric criticality. Two examples…

Symmetry plays a basic role in variational problems (settled e.g. in $\mathbb R^{n}$ or in a more general manifold), for example to deal with the lack of compactness which naturally appear when the problem is invariant under the action of a…

It is shown that if $S$ is a commuting family of weak$^{\ast }$ continuous nonexpansive mappings acting on a weak$^{\ast }$ compact convex subset $C$ of the dual Banach space $E$, then the set of common fixed points of $S$ is a nonempty…

Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…

We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow…

We show a few fixed point theorems for semigroups acting on weakly compact convex subsets of Banach spaces when $LUC(S), AP(S), WAP(S)$ or $WAP(S)\cap LUC(S)$ have a left invariant mean. In particular, we give a characterization of…

We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Previous attempts to analyse when these are minima ex- ist, but mainly…

It is known that the Cauchy's argument principle, applied to an holomorphic function $f$, requires that $f$ has no zeros on the curve of integration. In this short note, we give a generalization of such a principle which covers the case…

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White, we…

Given a compact Lie subgroup $G$ of the isometry group of a compact Riemannian manifold $M$ with a Riemannian connection $\nabla,$ it is introduced a $G-$symmetrization process of a vector field of $M$ and it is proved that the critical…

This paper deals with the following nonlocal system of equations: \begin{align}\tag{$\mathcal S$}\label{MAT1} (-\Delta_p)^s u = \frac{\alpha}{p_s^*}|u|^{\alpha-2}u|v|^{\beta}+f(x) \text{ in } \mathbb{R}^{d}, \, (-\Delta_p)^s v =…

We derive a variant of the nonsmooth maximum principle for problems with pure state constraints. The interest of our result resides on the nonsmoothness itself since, when applied to smooth problems, it coincides with known results.…

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators $A_j$ on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also…

Let f be local diffeomorphism between real Banach spaces. We prove that if the locally Lipschitz functional F(x)=1/2|f(x)-y|^2 satisfies the Chang Palais-Smale condition for all y in the target space of f, then f is a norm-coercive global…

In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic…

Considering that the Seiberg-Witten functional satisfies the Palais-Smale Condition, up to gauge equivalence, the Minimax Principle can be applied on the moduli space to prove the existence of critical points, which correspond to solutions…