In this paper we consider the discrete anisotropic boundary value problem using critical point theory. Thirstily we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at least one non-trivial solution. Secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at...

We consider a non-canonic field in the context of Starobinsky inflation. work Einstein-frame. In this frame, gravitational part action is equivalent to Hilbert–Einstein action, plus scalar called scalaron. investigate model with heavy scalaron trapped at effective potential minimum, where its fluctuations are negligible. To be more explicit, we Dirac–Born–Infeld (DBI) field, which usually consi...

An exact expression for the Green function of a purely fermionic system moving on the manifold R× ΣD−1, where ΣD−1 is a (D − 1)-torus, is found. This expression involves the bosonic analog of χn = e inθ corresponding to the irreducible representation for the n-th class of homotopy and in the fermionic case for D = 2 and 3, χn is a measure of the statistics of the particles. For higher dimension...

Given a complete non-compact surface Σ embedded in R, we consider the Dirichlet Laplacian in the layer Ω that is defined as a tubular neighbourhood of constant width about Σ. Using an intrinsic approach to the geometry of Ω, we generalise the spectral results of the original paper [1] by Duclos et al. to the situation when Σ does not possess poles. This enables us to consider topologically more...

Scalar delay differential equations with two delays are considered in this paper. Some monotonicity results permit to establish existence of non trivial slowly oscillating solutions.

We prove the existence and uniqueness of non-trivial stable solutions to Landau-Lifshitz-Maxwell equations with Dirichlet boundary condition for large anisotropies and small domains, where the domains are non-simply connected.