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 of Ambrosetti-Rabinowitz type.

Keywords

ANISOTROPIC ORLICZ-SOBOLEV SPACE EULER-LAGRANGE EQUATIONS MOUNTAIN PASS THEOREM PALAIS-SMALE CONDITION

Publication year

Publication language

angielski

Journal title / conference title

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Page numbers [from-to]

1 - 14

Author (2)



Organization unit

Katedra Analizy Nieliniowej i Statystyki

Faculty

Wydział Fizyki Technicznej i Matematyki Stosowanej