Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2014
Volume
Vol. 34
Number
No. 4
Description
Journal Volume
Opuscula Mathematica
Vol. 34 (2014)
Projects
Pages
Articles
Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex functions
(2014) Antczak, Tadeusz; Arana Jiménez, Manuel
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 sufficient optimality conditions under the assumptions that the functions constituting them are $B$-$(p,r)$-invex. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem in the sense of Mond-Weir is given and several duality results are established under $B$-$(p,r)$-invexity.
Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian
(2014) Candito, Pasquale; D’Aguí, Giuseppina
In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete $p$-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.
Remarks for one-dimensional fractional equations
(2014) Ferrara, Massimiliano; Molica Bisci, Giovanni
In this paper we study a class of one-dimensional Dirichlet boundary value problems involving the Caputo fractional derivatives. The existence of infinitely many solutions for this equations is obtained by exploiting a recent abstract result. Concrete examples of applications are presented.
Dynamic programming approach to structural optimization problem - numerical algorithm
(2014) Fulmański, Piotr; Nowakowski, Andrzej; Pustelnik, Jan
In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.
On a new critical point theorem and some applications to discrete equations
(2014) Galewski, Marek; Galewska, Elżbieta
Using the Fenchel-Young duality we derive a new critical point theorem. We illustrate our results with solvability for certain discrete BVP. Multiple solutions are also considered.