Email this article The Multiplicity of Positive Solutions to A Quasilinear Equation Generated By The Il′in–Caffarelli–Cohn–Nirenberg Inequality
- Authors: Nazarov A.I.1, Neterebskii B.O.2
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Affiliations:
- St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University
- Laser Systems LLC
- Issue: Vol 224, No 3 (2017)
- Pages: 448-455
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239618
- DOI: https://doi.org/10.1007/s10958-017-3427-z
- ID: 239618
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Abstract
The Euler–Lagrange equation for the functional related to the V. P. Il’in inequality also known as the Caffarelli–Kohn–Nirenberg inequality is considered. We prove that if the space dimension is even, then changing some parameters, one can obtain arbitrary many different positive solutions for this equation.
About the authors
A. I. Nazarov
St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University
Author for correspondence.
Email: al.il.nazarov@gmail.com
Russian Federation, St. Petersburg
B. O. Neterebskii
Laser Systems LLC
Email: al.il.nazarov@gmail.com
Russian Federation, St. Petersburg
