# Magdalena Chmara - Profil naukowy - MOST Wiedzy

## Wyszukiwarka ## mgr inż. Magdalena Chmara

### Asystent

Miejsce pracy
Gmach B
pokój 511 otwiera się w nowej karcie
Telefon
58 347 17 12
E-mail
magdalena.chmara@pg.edu.pl

### Wybrane publikacje

• #### Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations

In this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.

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• #### Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space

Using the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.

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• #### Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator

Using the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...

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