| Autor: |
Chen, Hua, Chen, Hong-Ge, Li, Jin-Ning, Liao, Xin |
| Zdroj: |
SCIENCE CHINA Mathematics; Mar2024, Vol. 67 Issue 3, p475-504, 30p |
| Abstrakt: |
In this paper, we study the semilinear subelliptic equation where is the self-adjoint Hörmander operator associated with the vector fields X = (Xl, X2, ..., Xm) satisfying the Hörmander's condition, is a Carathéodory function on Ω × ℝ, and Ω is an open bounded domain in ℝn with smooth boundary. Combining the perturbation from the symmetry method with the approaches involving the eigenvalue estimate and the Morse index in estimating the minimax values, we obtain two kinds of existence results for multiple weak solutions to the problem above. Furthermore, we discuss the difference between the eigenvalue estimate approach and the Morse index approach in degenerate situations. Compared with the classical elliptic cases, both approaches here have their own strengths in the degenerate cases. This new phenomenon implies that the results in general degenerate cases would be quite different from the situations in classical elliptic cases. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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