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Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution of the anisotropic discrete Dirichlet boundary value problem. Our results generalize and improve those of [16]. Math Subject Classifications: 39A10, 34B18, 58E30.

- Marek Galewski
- Applied Mathematics and Computation
- 2008

- Marek Galewski
- Applied Mathematics and Computation
- 2008

- Marek Galewski
- Applied Mathematics and Computation
- 2011

We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden-Fowler equation. A variational method is used in order to obtain a general scheme allowing for investigation the dependence on paramaters of discrete boundary value problems. MSC Subject Classification: 34B16, 39M10

- Marek Galewski, Joanna Smejda
- J. Computational Applied Mathematics
- 2010

- Marek Galewski
- 2011

Recently the classical variational problem for a Duffing type equation received again some attention. In [1], [2], [7], some variational approaches were used in order to receive the existence of solutions for both periodic and Dirichlet type boundary value problems. Mainly direct method is applied under various conditions pertaining to at most quadratic… (More)

- Leon Mikołajczyk, Tadeusz Antczak, Manuel Jiménez, Marek Galewski
- 2014

In this paper, we generalize the notion of B-(p, r)-invexity introduced by Antczak in [A class of B-(p; r)-invex functions and mathematical programming, J. Math. Anal. Appl. 286 (2003), 187–206] for scalar optimization problems to the case of a multiobjective variational programming control problem. For such nonconvex vector optimization problems, we prove… (More)

- Marek Galewski, Joanna Smejda
- Applied Mathematics and Computation
- 2013

We investigate the continuous dependence on parameters for the mountain pass solutions of second order discrete equations with p-Laplacian and Dirichlet type boundary conditions. We show that assumptions leading to the existence of nontrivial solutions lead also to its continuous dependence on parameters. We investigate also the uniqueness of solutions.… (More)

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)

Problems of reconstructing unknown characteristics of dynamical systems through measurements of a part of the phase coordinates are embedded into the theory of inverse problems of dynamics. This theory is intensively developed at the present time. One of approaches to solving similar problems based on methods of the theory of positional control [1] was… (More)