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Abstract
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.
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
no. 485,
pages 1 - 14,
ISSN: 0022-247X - Language:
- English
- Publication year:
- 2020
- Bibliographic description:
- Chmara M., Maksymiuk J.: Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator// JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS -Vol. 485,iss. 2 (2020), s.1-14
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.jmaa.2019.123809
- Verified by:
- Gdańsk University of Technology
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