The nature of critical points generated by a Ghoussoub's type min–max principle for locally Lipschitz continuous functionals fulfilling a weak Palais–Smale assumption, which contains the so-called non-smooth Cerami condition, is investigated. Two meaningful special cases are then pointed out; see Theorems 3.5 and 3.6.

On the structure of the critical set of non-differentiable functions with a weak compactness condition

In this paper, a new version of the restricted three-body problem is considered. That is the spatial quantized restricted three-body problem. The equations of motion of the infinitesimal body are constructed. The equilibria points in plane of primaries motion and out of plane are explored under the quantized gravitational potential effect. The permissible and forbidden regions of motion are also analyzed in both planes, with respect to relative small, middle and large values of the Jacobian constant. We observe that the size of permissible (forbidden) regions of motion are decreasing (increasing) with increasing the Jacobian constant values and vice versa. We demonstrate that the permissible regions of motion shrink with increasing the Jacobian constant value, and the infinitesimal body will be compelled to move in a surrounding region of one the primaries. It will has no free to switch or exchange its motion from one to other. Furthermore, we emphasize that, in spit of quantum corrections are tiny small effect, there is no warranty that the dynamical system properties are unaffected. Because there are changes in the locations of equilibria points and the regions of permissible motion, even which are very small. We think that these corrections may have considerable impact and can be tested within frame of small distances. Substantially, we are determine the parametric evolution of the equilibrium points of the system, along with the energetically allowed and forbidden regions of motion.

Analysis of the spatial quantized three-body problem

Existence of infinitely many periodic solutions for ordinary p-Laplacian systems☆

The existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via suband supersolution methods as well as variational techniques for nonsmooth functions.

/pdf/multiple-solutions-for-a-dirichlet-problem-with-p-laplacian-12o8cdr20r.pdf

MULTIPLE SOLUTIONS FOR A DIRICHLET PROBLEM WITH p-LAPLACIAN AND SET-VALUED NONLINEARITY

Molecular dynamic simulations of methane hydrate formation between solid surfaces: Implications for methane storage

A version of Zhong's coercivity result (1997) is established for nonsmooth functionals expressed as a sum &#x3A6;

/pdf/a-version-of-zhong-s-coercivity-result-for-a-general-class-40lsmgph5e.pdf

A version of Zhong′s coercivity result for a general class of nonsmooth functionals

We consider a generalization of the famous Lennard-Jones potential. To study the two-body problem associated to this potential, we use the foliations of the phase space by the invariant sets corresponding to the first integrals of energy and angular momentum. We investigate all possible situations created by the interplay among the constants of integration and the field parameters. We obtain the global flow, and illustrate it in both 3D and 2D. This flow exhibits a great variety of orbits, a homoclinic one included. All phase portraits are interpreted in terms of physical trajectories.

The two-body problem with generalized Lennard-Jones potential

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results on periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian

We study analytically the periodic solutions of a Hamiltonian in R 6 given by the kinetic energy plus a galactic potential, using averaging theory of first order The model perturbs a harmonic oscillator, and has been extensively used in order to describe local motion in galaxies near an equilibrium point

/pdf/periodic-solutions-of-a-galactic-potential-4t6slp424f.pdf

Periodic solutions of a galactic potential

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