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Non-existence of ground states and gap of variational values for 3D Sobolev critical nonlinear scalar field equations.
- Source :
-
Journal of Differential Equations . Oct2022, Vol. 334, p25-86. 62p. - Publication Year :
- 2022
-
Abstract
- In this paper, we consider minimization problems related to the combined power-type nonlinear scalar field equations involving the Sobolev critical exponent in three space dimensions. In four and higher space dimensions, it is known that for any frequency and any power of the subcritical nonlinearity, there exists a ground state. In contrast to those cases, when the space dimension is three and the subcritical power is three or less, we can show that there exists a threshold frequency, above which no ground state exists, and below which the ground state exists (see Theorems 1.1 and 1.2). Furthermore, we prove the difference between two typical variational problems used to characterize the ground states (see Theorem 1.3). [ABSTRACT FROM AUTHOR]
- Subjects :
- *EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 334
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 158055328
- Full Text :
- https://doi.org/10.1016/j.jde.2022.06.016