Eigenvalue problems in anisotropic Orlicz–Sobolev spaces

We establish sufficient conditions for the existence of solutions to a class of nonlinear eigenvalue problems involving nonhomogeneous differential operators in Orlicz–Sobolev spaces. To cite this article: M. Mih?ilescu et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Inequality problems with Nonlocally Lipschitz Energy Functional: Existence Results and Applications to Nonsmooth Mechanics

We give an existence result for a double eigenvalue problem in Hemivariational Inequalities whose energetic functional is not locally Lipschitz. It is used a finite dimensional approach based on Kakutani's fixed point theorem.     

通过同步实现从混沌到有序的转变

本文旨在研究连续的混沌系统是否存在“混沌＋混沌=有序”的现象．证明了两个双向耦合的连续混沌系统在一些情况下可产生有序的动力学行为．作为例子，通过选取适当的耦合参数使Lorenz系统以及Chen和Lee引入的混沌系统同步，进而对同步系统的动力学行为进行了理论分析和数值模拟．结果表明，逐渐改变参数，系统实现了从混沌到有序的过渡．     

Concentration phenomena in nonlinear eigenvalue problems with variable exponents and sign-changing potential

In this paper we establish the concentration of the spectrum in an unbounded interval for a class of eigenvalue problems involving variable growth conditions and a sign-changing potential. We also study the optimization problem for the particular eigenvalue given by the infimum of the associated Rayleigh quotient when the variable potential lies in a bounded, closed and convex subset of a certain variable exponent Lebesgue space.     

Effective results on compositions of nonexpansive mappings

This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the setting of (r,δ)$(r,\delta )$-convex spaces, a class of geodesic spaces which generalizes metric spaces with a convex geodesic bicombing.     

An application of proof mining to nonlinear iterations

In this paper we apply methods of proof mining to obtain a highly uniform effective rate of asymptotic regularity for the Ishikawa iteration associated with nonexpansive self-mappings of convex subsets of a class of uniformly convex geodesic spaces. Moreover, we show that these results are guaranteed by a combination of logical metatheorems for classical and semi-intuitionistic systems.     

Multiplicity results for elliptic fractional equations with subcritical term

In the present paper, by using variational methods, we study the existence of multiple nontrivial weak solutions for parametric nonlocal equations, driven by the fractional Laplace operator \({(-\Delta)^{s}}\) , in which the nonlinear term has a sublinear growth at infinity. More precisely, a critical point result for differentiable functionals is exploited, in order to prove the existence of an open interval of positive eigenvalues for which the treated problem admits at least two nontrivial weak solutions in a suitable fractional Sobolev space.     

Multiple solutions of hemivariational inequalities with area-type term

Hemivariational inequalities containing both an area-type and a non-locally Lipschitz term are considered. Multiplicity results are obtained by means of techniques of nonsmooth critical point theory. Received: December 24, 1998 / Accepted: October 1, 1999     

In memory of professor D. D. Ivanenko

In memory of professor D. D. Ivanenko