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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:485

Article

Chmara, M.¹  Maksymiuk, J.¹ 

[1] Gdansk Univ Technol, Dept Tech Phys & Appl Math, Narutowicza 11-12, PL-80233 Gdansk, Poland

关键词: Anisotropic Orlicz-Sobolev space;    Euler-Lagrange equations;    Mountain Pass Theorem;    Palais Smale condition;   

DOI  :  10.1016/j.jmaa.2019.123809

来源: Elsevier

【 摘 要 】

Using the Mountain Pass Theorem we show that the problem {(d/dt L-v (t, u(t), (u) over dot(t)) = L-x(t, u(t), (u) over dot(t))) for a.e. t is an element of [a, b] u(a) = u(b) = 0 has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian L = F(t, x, v) + V (t, x) + ( f (t), x) with growth conditions determined by anisotropic G-function and some geometric conditions of Ambrosetti-Rabinowitz type. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free