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Quasilinear Schrödinger equations with bounded coefficients.
- Source :
- Nonlinearity; Oct2022, Vol. 35 Issue 10, p4939-4985, 47p
- Publication Year :
- 2022
-
Abstract
- We study quasilinear elliptic equations of the form â' div A (u) ⇠u + 1 2 A ′ (u) | ⇠u | 2 + V (x) u = h (u) , u â H 1 ( R N ) , where N â©ľ 3 , A â C 1 (R , R + ) is a bounded function, V (x) is allowed to be singular at the origin, and h â C (R , R) is a general nonlinearity. Such type of equations has been derived as models of several physical phenomena corresponding to various types of A. Despite the lack of a priori compactness condition for the energy functional, we develop a new variational approach to deal with the issues of multiple radial solutions, nonradial solutions and sign-changing solutions. [ABSTRACT FROM AUTHOR]
- Subjects :
- PHENOMENOLOGICAL theory (Physics)
EQUATIONS
ELLIPTIC equations
SCHRODINGER equation
Subjects
Details
- Language :
- English
- ISSN :
- 09517715
- Volume :
- 35
- Issue :
- 10
- Database :
- Complementary Index
- Journal :
- Nonlinearity
- Publication Type :
- Academic Journal
- Accession number :
- 159320015
- Full Text :
- https://doi.org/10.1088/1361-6544/ac821b