Damped vibration problems with nonlinearities being sublinear at both zero and infinity

In this paper, we study a class of damped vibration problems with nonlinearities being sublinear at both zero and infinity, and we obtain infinitely many nontrivial periodic solutions by using a variant fountain theorem. To the best of our knowledge, there is no published result concerning this case by this method. Copyright © 2015 John Wiley & Sons, Ltd.     

A control scheme based on ER-materials for vibration attenuation of dynamical systems

Based on a bang-bang control scheme acting on so called “electrorheological” fluids (ER-fluids), a vibration suppression method is proposed for a class of n-dimensional systems subjected to unknown perturbations. The proposed controller relates to robustness vis-a-vis unknown but bounded disturbances. Two approaches for designing the control scheme are presented and compared. On the one hand we employ Lyapunov stability theory; on the other hand there is an obvious reason for minimizing rate of energy change due to the spring/damper elements by varying the ER-fluid properties appropriately. The system under investigation is an n-degree of freedom one consisting of masses and spring/damper elements. The spring/damper elements contain an ER-fluid; their stiffness and damping properties are changed by varying an imposed electrical field. The changes in spring and damping properties can be effected in microseconds since the control does not involve the separate dynamics (inertia) of usual actuators. Detailed derivations are presented for a two-dimensional case and simulations are carried out for examples of smooth periodic and discontinuous periodic excitation forces.     

A non-smooth three critical points theorem with applications in differential inclusions

We extend a recent result of Ricceri concerning the existence of three critical points of certain non-smooth functionals. Two applications are given, both in the theory of differential inclusions; the first one concerns a non-homogeneous Neumann boundary value problem, the second one treats a quasilinear elliptic inclusion problem in the whole \mathbb R^N{\mathbb R^N}.     

Experimental study of steady-state localization in coupled beams with active nonlinearities

Summary Steady-state nonlinear motion confinement is experimentally studied in a system of weakly coupled cantilever beams with active stiffness nonlinearities. Quasistatic swept-sine tests are performed by periodically forcing one of the beams at frequencies close to the first two closely spaced modes of the system, and experimental nonlinear frequency response curves for certain nonlinearity levels are generated. Of particular interest is the detection of strongly localized steady-state motions, wherein vibrational energy becomes spatially confined mainly to the directly excited beam. Such motions exist in neighborhoods of strongly localized antiphase nonlinear normal modes (NNMs) which bifurcate from a spatially extended NNM of the system. Steady-state nonlinear motion confinement is an essentially nonlinear phenomenon with no counterpart in linear theory, and can be implemented in vibration and shock isolation designs of mechanical systems.Presently Assistant Professor of Aerospace and Mechanical Engineering, Boston University (from January 1995).     

A Robin boundary problem with Hardy potential and critical nonlinearities

Let Ω be a bounded domain with a smooth C ² boundary in ℝⁿ (n ≥ 3), 0 ∈ , and υ denote the unit outward normal to ∂Ω. In this paper, we are concerned with the following class of boundary value problems:

A proximal gradient method for control problems with non-smooth and non-convex control cost

Computational Optimization and Applications - We investigate the convergence of the proximal gradient method applied to control problems with non-smooth and non-convex control cost. Here, we focus...     

Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces

We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties.     

A new perturbation solution for systems with strong quadratic and cubic nonlinearities

The new perturbation algorithm combining the method of multiple scales (MS) and Lindstedt–Poincare techniques is applied to an equation with quadratic and cubic nonlinearities. Approximate analytical solutions are found using the classical MS method and the new method. Both solutions are contrasted with the direct numerical solutions of the original equation. For the case of strong nonlinearities, solutions of the new method are in good agreement with the numerical results, whereas the amplitude and frequency estimations of classical MS yield high errors. For strongly nonlinear systems, exact periods match well with the new technique while there are large discrepancies between the exact and classical MS periods. Copyright © 2009 John Wiley & Sons, Ltd.     

A remark on connection between conjugacy of half-linear differential equation and equation with mixed nonlinearities

In this paper new criteria for conjugacy of half-linear ordinary differential equations are derived by using a Riccati transformation. These criteria are used to derive nonexistence and oscillation results for an equation with mixed nonlinearities, which is viewed as a perturbation of a half-linear equation.     

Supply chain performance evaluation using fuzzy network data envelopment analysis: a case study in automotive industry

Supply chain performance evaluation problems are evaluated using data envelopment analysis. This paper proposes a fuzzy network epsilon-based data envelopment analysis for supply chain performance evaluation. In the common data envelopment analysis models which are used for evaluation of decision-maker units efficiency, there are several inputs and outputs. One of the bugs of such models is that the intermediate products and linking activities are overlooked. Considering these intermediate activities and products, the current study evaluates the performance of decision-maker units in an automotive supply chain. There are ten decision-maker units in the supply chain in which there are three suppliers, two manufacturers, two distributors, and four customers. Moreover, the overall efficiency of input-oriented (input-based) model and input-oriented divisional efficiency are calculated. In order to improve the efficiencies, the projections onto the frontiers are obtained by using the outputs of the solved model and Lingo software. In order to show the applicability of the proposed model, it is applied on automotive industry, as a case study, to evaluate supply chain performance. Then, the overall efficiencies of DMUs and each sections (divisions) of DMUs were calculated separately. Therefore, every organization can apply this evaluation method for improving the performance of alternative factors.

     

A global compact result for a semilinear elliptic problem with Hardy potential and critical nonlinearities on R~N

In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/(N-2) is the critical Sobolev exponent, 2 q 2 , 0≤μ μˉ=(N-2)2_4 , a(x), k(x) ∈ C(RN ). Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a(x) and k(x).     

Indefinite quasilinear elliptic problems with subcritical and supercritical nonlinearities on unbounded domains

By using the fibering method, we study the existence of non-negative solutions for a class of indefinite quasilinear elliptic problems on unbounded domains with noncompact boundary, in the presence of competing subcritical and supercritical lower order nonlinearities.     

On semilinear elliptic equations with sublinear and superlinear nonlinearities in rN

The existence of infinitely many solutions for the equation     

The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains

We introduce certain Sobolev-Besov spaces which are particularly well adapted for measuring the smoothness of data and solutions of mixed boundary value problems in Lipschitz domains. In particular, these are used to obtain sharp well-posedness results for the Poisson problem for the Laplacian with mixed boundary conditions on bounded Lipschitz domains which satisfy a suitable geometric condition introduced by R.Brown in (1994). In this context, we obtain results which generalize those by D.Jerison and C.Kenig (1995) as well as E.Fabes, O.Mendez and M.Mitrea (1998). Applications to Hodge theory and the regularity of Green operators are also presented.