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The paper discusses a method of auxiliary controlled models and the application of this method to solving problems of dynamical reconstruction of an unknown coordinate in a nonlinear system of differential equations. The solving algorithm, which is stable with respect to informational noises and computational errors, is presented.
In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function α , a nonlinear term f , and a numerical parameter λ : ∆ (α (k) |∆u(k − 1)| p(k−1)−2 ∆u(k − 1)) + λf (k, u(k)) = 0, k ∈ [1, T ]. We derive the intervals of a numerical parameter λ for which the considered BVP has at least 1, exactly 1, or at least 2(More)
Using the Fenchel-Young duality and mountain pass geometry we derive a new multiple critical point theorem. In a finite dimensional setting it becomes three critical point theorem while in an infinite dimensional case we obtain the existence of at least two critical points. The applications to anisotropic problems show that one can obtain easily that all(More)