Electron. J. Differential Equations, Vol. 2018 (2018), No. 140, pp. 1-16.

Existence of minimizers of multi-constrained variational problems for product functions

Huda Al Saud, Hichem Hajaiej

We prove the existence of minimizers of a class of multi-constrained variational problems in which the non linearity involved is a product function not satisfying compactness, monotonicity, neither symmetry properties. Our result cannot be covered by previous studies that considered only a particular class of integrands. A key step is establishing the strict sub-additivity condition in the vectorial setting. This inequality is also interesting in itself.

Submitted February 23, 2018. Published July 8, 2018.
Math Subject Classifications: 74G65, 35J62, 35A15, 35B06, 58E05.
Key Words: Multi-constrained; variational; elliptic systems; non-compact.

Show me the PDF file (256 KB), TEX file for this article.

  Huda Al Saud
Department of mathematics
College of Science, King Saud University
Riyadh, Saudi Arabia
email: halsaud@ksu.edu.sa
Hichem Hajaiej
California State University Los Angeles
5151 University Drive
Los Angeles, CA 90032, USA
email: hhajaie@calstatela.edu

Return to the EJDE web page