In this article, we show the existence of at least three solutions to a Navier boundary problem involving the p(x)-biharmonic operator. The technical approach is mainly base on a three critical points theorem by Ricceri.

In this paper, we establish the existence of at least three solutions to a Navier boundary problem involving the biharmonic equation. The technical approach is mainly base on a three critical points theorem of B. Ricceri. AMS Subject Classifications: 34B15.

By means of a three critical points theorem proposed by Brezis and Nirenberg and a general version of Mountain Pass Theorem, we obtain some multiplicity results for periodic solutions of a fourth-order discrete Hamiltonian system ∆u(t− 2) +∇F (t, u(t)) = 0, for all t ∈ Z.

We investigate the density of critical positions, that is, the ratio between the number of critical positions and the number of all positions of a word, in infinite sequences of words of index one, that is, the period of which is longer than half of the length of the word. On one hand, we considered words with the lowest possible number of critical points, namely one, and show, as an example, t...

We give an alternative proof of the Benedicks-Carleson theorem on the existence of strange attractors in Hénon-like maps in the plane. To bypass a huge inductive argument, we introduce an induction-free explicit definition of dynamically critical points. The argument is sufficiently general and in particular applies to the case of non-invertible maps as well. It naturally raises the question of...

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

Some multiplicity results are obtained for periodic solutions of the nonautonomous superquadratic second-order discrete Hamiltonian systems Duðt 1Þ þ rF ðt; uðtÞÞ 1⁄4 0 8t 2 Z 0096-3 doi:10. q Sup Outsta * Co E-m Plea Com by using critical point theory, especially, a three critical points theorem proposed by Brezis and Nirenberg. 2007 Elsevier Inc. All rights reserved.