This work is devoted to the study of the existence of at least one (non-zero) solution to a problem involving the discrete p-Laplacian. As a special case, we derive an existence theorem for a second-order discrete problem, depending on a positive real parameter a, whose prototype is given by Duðk 1Þ 1⁄4 af ðk;uðkÞÞ; 8k 2 Z1⁄21; T ; uð0Þ 1⁄4 uðT þ 1Þ 1⁄4 0: ( Our approach is based on variational...

This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points. To illustrate our approach, two examples are discussed in detail.

In abstract terms, the Calculus of Variations is a subject concerned with max/min problems for a real-valued function of several variables. Given a vector space V and a function Φ:V → R, we explore the theory and practice of minimizing Φ[x] over x ∈ V . Additional interest and power comes from allowing • dim(V ) = +∞, • constrained minimization, where the choice variable x must lie in some prea...

In this paper, we consider the existence of multiple nontrivial solutions for some fourth order quasilinear elliptic boundary value problems. The weak solutions are sought by using variational methods.

We study the existence of n distinct pairs of nontrivial solutions for impulsive differential equations with Dirichlet boundary conditions by using variational methods and critical point theory.

In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation −∆pu = |u| ∗ u + λf(x, u) in a smooth bounded domain Ω of R with homogeneous Dirichlet boundary conditions on ∂Ω, where p = Np/(N − p) is the critical Sobolev exponent and ∆pu = div(|∇u|∇u) is the p−laplacian. The proof is based on variational arguments and the classical con...

Article history: Received 13 June 2013 Accepted 3 September 2015 Available online 19 January 2016 Communicated by L. Gross MSC: primary 49R05 secondary 47A56, 47A10

The Evans function is known as a helpful tool for locating the spectrum of some variational diierential operators. This is of special interest regarding the stability analysis of traveling waves, such as reaction-diiusion waves, solitary waves, viscous shock waves, etc., and has been used in numerous contexts. The rst aim of this paper is to present an overview of the various ways to deene an E...

In contrast to the quite unique entropy concept useful for systems in (local) thermodynamic equilibrium, there is a variety of quite distinct nonequilibrium entropies, reflecting different physical points. We disentangle these entropies as they relate to heat, fluctuations, response, time-asymmetry, variational principles, monotonicity, volume contraction or statistical forces. However, not all...