For a class of second order quasilinear elliptic equations we establish the existence of two non-negative weak solutions of the Dirichlet problem on a bounded domain, Ω. Solutions of the boundary value problem are critical points of C−functional on H 0 (Ω). One solution is a local minimum and the other is of mountain pass type. Mathematics Subject Classification (2000). Primary 35J62; Secondary...

In this paper, we consider the existence of multiple positive solutions for Kirchhoff-Schrödinger-Poisson system with the nonlinear term containing both general singularity and quasicritical nonlinearity. By combining the variational method with the perturbation method, we obtain the existence of two positive solutions with the parameter λ small enough. One of the solutions is the local minimum...

We consider the problem of constructing protocols for secure computation that achieve strong concurrent and composable notions of security in the plain model. Unfortunately UC-secure secure computation protocols are impossible in this setting, but the Angel-Based Composable Security notion offers a promising alternative. Until now, however, under standard (polynomialtime) assumptions, only prot...

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...

In this paper we study a quasilinear elliptic system coupled by Schrödinger equation with p-Laplacian operator and Poisson equation. Some scaling transformation ingenious methods are applied to produce the bounded Palais-Smale sequences existence of nontrivial solutions for is obtained mountain pass theorem.

We offer a new proof of the Furstenberg-Katznelson multiple recurrence theorem for several commuting probability-preserving transformations T1, T2, . . . , Td : Z y (X,Σ, μ) ([6]), and so, via the Furstenberg correspondence principle introduced in [5], a new proof of the multi-dimensional Szemerédi Theorem. We bypass the careful manipulation of certain towers of factors of a probability-preserv...