On the existence and the stability of solutions for higher-order semilinear Dirichlet problems

We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.     

On the existence of solutions for a system of difference equations with non-monotone nonlinearity

We derive a dual variational method in order to obtain the existence of a bounded solution to a certain nonlinear system with non-monotone nonlinearities. We consider such a system representing a difference equation arising from evaluating some Dirichlet boundary value problems.     

Saddle-point solutions to Dirichlet problems on the Sierpiński gasket

We provide sufficient conditions for the existence of saddle-point solutions to a system driven by the weak Laplacian on the Sierpiński gasket. We analyze also its stability by proving its continuous dependence on parameters.     

On the existence and stability of higher order Dirichlet problems

We provide the existence and the stability results for higher order Dirichlet problems with convex nonlinearity which satisfies general local growth conditions. We construct a dual variational method and investigate relations between primal action functional and dual action functional.     

On the system of anisotropic discrete BVPs

We investigate the existence of solutions of the system of anisotropic discrete boundary value problems using critical point theory. We apply direct variational approach, the Ky Fan min–max inequality and the mountain pass lemma.     

A note on a global invertibility of mappings on Rn

We provide sufficient conditions for a mapping f : Rⁿ → Rⁿ to be a global di?eomorphism in case f need not be continuously di?erentiable. Instead it is assumed to be strictly (Hadamard-like) and Fréchet di?erentiable. We use classical local invertibility conditions together with the non-smooth critical point theory.     

On a global implicit function theorem and some applications to integro-differential initial value problems

We generalize a recent global implicit function theorem from [8] to the case of a mapping acting between Banach spaces. Considerations related to duality mapping and to certain auxiliary functional are used in the proof together with the local implicit function theorem and mountain pass geometry. An application to integro-differential systems is given.     

Chatter Vibration Surveillance by the Optimal-linear Control of Spindle Speed and Randomly Varying Spindle Speed

Tool-workpiece relative vibration plays principal role during the process of milling with slender ball end mills. Due to certain conditions, a loss of stability and generation of self-excited chatter vibration will appear. The paper is devoted to a new approach towards vibration surveillance of rotating tools in modern milling machines. Dynamic analysis of a slender ball end milling process has been performed and dynamics of controlled structure is described. In order to reduce vibration level, instantaneous change in the spindle speed appears as control command, and thus the method of vibration surveillance by the spindle speed optimal-linear control has been developed. Due to quality of machined surface being worse while milling with high tilting angle of the tool, the other method of milling with randomly varying spindle speed is presented. It allows us to maintain a high efficiency of surveillance without worsening of the machining quality. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Insight into polymorphism of the ethosuximide (ETX)

Rich polymorphism of ethosuximide compound (ETX) is described in detail using complementary thermal analysis methods. The paper shows as well the results of differential scanning calorimetry (DSC), of polarizing microscope observations (POM) and of X-ray diffraction (XRD) measurements taken using horizontal rotating capillary method. Molecular structure of ethosuximide favors appearance of a conformationally disordered (CONDIS) crystal phase CrI in its polymorphism. Ethosuximide is a good glass former, and glass of the CrI phase was observed even for 5 °C min^?1 rate of cooling. Moreover, monotropic plastic crystal CrII phase was observed during heating above the CrI temperature range.