Abstract
We are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic -Laplacian operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev space, and by using a consequence of the local minimum theorem due to Bonanno, we establish existence of at least one weak solution under algebraic conditions on the nonlinear term. Also, we discuss existence of at least two weak solutions for the problem, under algebraic conditions including the classical Ambrosetti-Rabinowitz condition on the nonlinear term. Furthermore, by employing a three critical point theorem due to Bonanno and Marano, we guarantee the existence of at least three weak solutions for the problem in a special case.
Recommended Citation
M. Bohner et al., "Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian," Nonautonomous Dynamical Systems, vol. 7, no. 1, pp. 53 - 64, De Gruyter, Jan 2020.
The definitive version is available at https://doi.org/10.1515/msds-2020-0108
Department(s)
Mathematics and Statistics
Publication Status
Open Access
Keywords and Phrases
-Laplacian operator; anisotropic variable exponent Sobolev space; Neumann elliptic problem; variational principle; weak solution
International Standard Serial Number (ISSN)
2353-0626
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2024 The Authors, All rights reserved.
Publication Date
01 Jan 2020
