To Fu Ma

Positive solutions for a nonlinear nonlocal elliptic transmission problem

We show the existence and nonexistence of positive solutions for a transmission problem given by a system of two nonlinear elliptic equations of Kirchhoff type.

Iterative solutions for a beam equation with nonlinear boundary conditions of third order

A fourth-order differential equation with nonlinear boundary conditions modeling beams on elastic foundations is considered. Iterative solutions are proved through the contraction principle. Some numerical simulations are also provided.

Existence results for a model of nonlinear beam on elastic bearings

Abstract We study the existence of solutions of the nonlinear fourth-order equation of Kirchhoff type under nonlinear boundary conditions which models the deformations of beams on elastic bearings.

Perturbations near resonance for the p-Laplacian in ℝN

We study a multiplicity result for the perturbed p-Laplacian equation −Δpu−λg(x)|u|p−2u=f(x,u)

Multiple solutions for a class of nonlinear boundary value problems near resonance: a variational approach

Abstract A variational approach is given to the existence of multiple solutions for some nonlinear boundary value problems near resonance at the first eigenvalue.

Long-time dynamics for a class of Kirchhoff models with memory

This paper is concerned with a class of Kirchhoff models with memory effects utt+αΔ2u−div(|∇u|p−2∇u)−∫0∞μ(s)Δ2u(t−s)ds−Δut+f(u)=h, defined in a bounded domain of RN. This non-autonomous equation corresponds to a viscoelastic version of Kirchhoff models arising in dynamics of elastoplastic flows and plate vibrations. Under assumptions that the exponent p and the growth of f(u) are up to the critical range, it turns out that the model corresponds to an autonomous dynamical system in a larger phase space, by adding a component which describes the relative displacement history. Then the existence of a global attractor is granted. Furthermore, in the subcritical case, this global attractor has finite Hausdorff and fractal dimensions.

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method.

Positive solutions for a fourth order equation with nonlinear boundary conditions

Existence of positive solutions for a fourth order equation with nonlinear boundary conditions, which models deformations of beams on elastic supports, is considered using fixed points theorems in cones of ordered Banach spaces. Iterative and numerical solutions are also considered.

Positive solutions for a nonlinear Kirchhoff type beam equation

The existence of two solutions, a positive and a negative, for a nonlinear fourth order equation with nonlinear boundary conditions is considered. The problem models the bending equilibrium of extensible beams on nonlinear elastic foundations.

A thermoelastic system of memory type in noncylindrical domains

In this paper, we consider a hyperbolic thermoelastic system of memory type in domains with moving boundary. The problem models vibrations of an elastic bar under thermal effects according to the heat conduction law of Gurtin and Pipkin. Global existence is proved by using the penalty method of Lions.