Local uniqueness for the multi-bump solutions to the problem of Ambrosetti-Prodi type

作者：Chen, Haixia; Chen, Mengyao^*; Li, Qi

来源：Journal of Mathematical Physics, 2022, 63(4): 041512.

DOI：10.1063/5.0065173

• LAZER-MCKENNA CONJECTURE
• RADIALLY SYMMETRIC-SOLUTIONS
• SCALAR CURVATURE PROBLEM
• ELLIPTIC PROBLEM
• POSITIVE SOLUTIONS
• PEAK SOLUTIONS
• BOUND-STATES
• EXACT NUMBER
• EQUATION

We consider a type of elliptic problem of Ambrosetti-Prodi type with the subcritical Sobolev exponent. Based on the local type of Pohozaev identities, we prove the uniqueness for multi-bump solutions constructed by Dancer and Yan [J. Differ. Equations 210, 317-351 (2005)]. As a consequence, we obtain the local uniqueness for the problem of Ambrosetti-Prodi type.& nbsp;Published under an exclusive license by AIP Publishing.