Estimation of fixed points for nonlinear time series

Identification of fixed points is very important in dynamic systems analysis. One method used is based on polynomial regression. In this article, we show that methods other than that of Aguirre and Souza can be more accurate if the classical assumptions for regression are violated. Simulation results reveal that an artificial neural network (ANN) is more precise than the Aguirre and Souza method, which is based on cluster expansion method. Overall, ANN is the best method for finding fixed (equilibrium) points of nonlinear time series, followed by nonparametric regression in terms of accuracy. For larger sample sizes, ANN estimates are generally accurate and the method is robust to changes in the signal/noise ratio. © 2013 Wiley Periodicals, Inc. Complexity 19: 30–39, 2014     

Multiplicity results for p(x)-biharmonic equations with Navier boundary conditions

This paper deals with the existence of solutions for a class of p(x)-biharmonic equations with Navier boundary conditions. The approach is based on variational methods and critical point theory. Indeed, we investigate the existence of two solutions for the problem under some algebraic conditions with the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Moreover, by combining two algebraic conditions on the nonlinear term which guarantee the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of the third solution for the problem.     

Existence of one non‐trivial anti‐periodic solution for second‐order impulsive differential inclusions

The existence of one non‐trivial solution for a second‐order impulsive differential inclusion is established. More precisely, a recent critical point result is exploited, in order to prove the existence of a determined open interval of positive eigenvalues for which the considered problem admits at least one non‐trivial anti‐periodic solution. Copyright © 2017 John Wiley & Sons, Ltd.     

Variational approaches to p-Laplacian discrete problems of Kirchhoff-type

Critical point results for Kirchhoff-type discrete boundary value problems are exploited in order to prove that a suitable class possesses at least one solution under an asymptotical behaviour of the potential of the nonlinear term at zero, and also possesses infinitely many solutions under some hypotheses on the behaviour of the potential of the nonlinear term at infinity. Some recent results are extended and improved. Some examples are presented to demonstrate the applications of our main results.     

Infinitely Many Solutions for a Mixed Doubly Eigenvalue Boundary Value Problem

In this paper, we prove the existence of infinitely many weak solutions for a mixed doubly eigenvalue boundary value problem. The approach is based on variational methods.     

Multiple solutions for partial discrete Dirichlet problems depending on a real parameter

In this paper we establish the existence of multiple solutions for a partial discrete Dirichlet problem depending on a real parameter. More precisely, under appropriate assumptions on the nonlinearities, we determine exact collections of parameters such that the treated problems admit at least three solutions.     

Multiple Solutions for Systems of Sturm–Liouville Boundary Value Problems

In this paper, the authors discuss the existence of multiple solutions to a class of second-order Sturm–Liouville boundary value systems. Their proofs are based on variational methods and critical point theory.     

Variational approaches to impulsive elastic beam equations of Kirchhoff type

In this paper, we study the existence of multiple solutions for impulsive fourth-order differential equations of Kirchhoff type. Using a variational method and some critical points theorems, we obtain some new criteria for guaranteeing that impulsive fourth-order differential equations of Kirchhoff type have three and infinitely many solutions. Some recent results are extended and improved. Some examples are presented to demonstrate the applications of our main results.     

Existence of non-trivial solutions for systems of n fourth order partial differential equations

In this paper, employing a very recent local minimum theorem for differentiable functionals due to Bonanno, the existence of at least one nontrivial solution for a class of systems of n fourth order partial differential equations coupled with Navier boundary conditions is established.