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Anti-periodic solutions to a parabolic hemivariational inequality

Jong Yeoul Park, Hyun Min Kim, Sun Hye Park (2004)

Kybernetika

In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form b ( u ) , where b L loc ( R ) . Extending b to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.

Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential.

Charles L. Fefferman, Luis A. Seco (1993)

Revista Matemática Iberoamericana

In [FS1] we announced a precise asymptotic formula for the ground-state energy of a non-relativistic atom. The purpose of this paper is to establish an elementary inequality that plays a crucial role in our proof of that formula. The inequality concerns the Thomas-Fermi potentialVTF = -y(ar) / r, a > 0, where y(r) is defined as the solution of⎧   y''(x) = x-1/2y3/2(x),⎨   y(0) = 1,⎩   y(∞) = 0.

Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats

Shin-Ichiro Ei, Kota Ikeda, Masaharu Nagayama, Akiyasu Tomoeda (2014)

Mathematica Bohemica

Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices to investigate a linearized...

Application of a second order VSC to nonlinear systems in multi-input parametric-pure-feedback form

Antonella Ferrara, Luisa Giacomini (2000)

Kybernetika

The use of a multi-input control design procedure for uncertain nonlinear systems expressible in multi-input parametric-pure feedback form to determine the control law for a class of mechanical systems is described in this paper. The proposed procedure, based on the well-known backstepping design technique, relies on the possibility of extending to multi-input uncertain systems a second order sliding mode control approach recently developed, thus reducing the computational load, as well as increasing...

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