Abstract
The paper is concerned with the existence of nontrivial solutions of the obstacle problem: u ε K: ∫Ω ▽u▽ (v - u) dx - λ ∫ Ω u (v - u) dx ≥ ∫ Ω p (x, u) (v - u) dx ∀x ε K, where K = {v ε Ho1(Ω): v ≤ Ψ a.e. on Ω}. By using a generalized mountain pass theorem for inequalities, we prove, subject to some restrictions on the obstacle Ψ, the existence of nontrivial solutions of the above inequality.
Recommended Citation
V. K. Le and K. Schmitt, "On the Existence of Nontrivial Solutions to Some Elliptic Variational Inequalities," Advanced Nonlinear Studies, vol. 2, no. 3, pp. 251 - 262, De Gruyter, Jan 2002.
The definitive version is available at https://doi.org/10.1515/ans-2002-0303
Department(s)
Mathematics and Statistics
Keywords and Phrases
Obstacle problems; Variational inequalities
International Standard Serial Number (ISSN)
1536-1365
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2024 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Jan 2002
