Abstract We consider a Dirichlet type problem for nonlinear, nonlocal equation driven by the degenerate fractional p -Laplacian, whose reaction combines sublinear term depending on positive parameter and an asymmetric perturbation (superlinear at infinity, most linear negative infinity). By means of critical point theory Morse theory, we prove that, small enough values parameter, such admits le...

Abstract We prove the stability of solitons Maxwell–Lorentz equations with extended charged rotating particle. The are solutions which correspond to uniform rotation To stability, we construct Hamilton–Poisson representation system. construction relies on Hamilton least action principle. constructed structure is degenerate and admits a functional family Casimir invariants. This allows us Lyapun...

In the visualization of the topology of second rank symmetric tensor fields in the plane one can extract some key points (degenerate points), and curves (separatrices) that characterize the qualitative behaviour of the whole tensor field. This can provide a global structure of the whole tensor field, and effectively reduce the complexity of the original data. To construct this global structure ...

Abstract We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n → 0, and consider the regular case...

Let H be a Hilbert space and J ∈ C(H, ). Denote δJ its Frechet derivative and J ′ its gradient. The objective of this research is to develop computational theory and methods for finding multiple critical points, i.e., solutions to the Euler-Lagrange equation J (u) = 0. A critical point u is nondegenerate if J (u) is invertible. Otherwise u is degenerate. The first candidates for a critical poin...

We study point-sphere and point-plane incidences in three-dimensional space. In particular, for 1 < k < n, we say that a set of spheres (resp., planes) is k-non-degenerate if no circle is contained in k spheres of the set (resp., if no line is contained in k planes of the set). We prove that, for every ε > 0, the number of incidences between a set of m points and a k-non-degenerate set of n sph...