Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
Classical Analysis and ODEs
2019-03-19 v1
Abstract
Using the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\mathcal{L}_v(t,u(t),\dot u(t))=\mathcal{L}_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 with growth condition determined by anisotropic G-function and some geometric condition of Ambrosetti-Rabinowitz type.
Cite
@article{arxiv.1903.07150,
title = {Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator},
author = {M. Chmara and J. Maksymiuk},
journal= {arXiv preprint arXiv:1903.07150},
year = {2019}
}