The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the p(x)-biharmonic operator with Navier boundary value conditions. The proof is mainly based on a three critical points theorem due to B. Ricceri [Nonlinear Anal. 70 (2009), 3084-3089].

No abstract

In this paper the problems of the existence and stability of periodic solutions of neutral-type inertial neural networks with time-varying delays are discussed by applying Mawhin’s continuation theorem and Lyapunov functional method. Finally, two numerical examples are given to illustrate our theoretical results.

Consider the simultaneous identification of the initial field and spatial heat source for heat conduction process from extra measurements with the two additional measurement data at different times. The uniqueness and conditional stability for this inverse problem are established by using the properties of a parabolic equation and the representation of solution after reforming the equation. By combining the least squares method with the regularization technique, the inverse problem is transformed into an optimal control problem. Based on the existence and uniqueness of the minimizer of the cost functional, an alternative iteration process is built to solve this optimizing problem by the variational adjoint method. The negative gradient direction is selected as the first search direction. For further iterations, the alternative iteration algorithm is used for the initial field and heat source identification. The efficiency of the proposed scheme is tested by the numerical simulation experiments.

No abstract