Abstract
This paper aims to give an affirmative answer to a conjecture raised by Soave (2020) [25] and considers the qualitative properties of normalized solutions to Sobolev critical/subcritical Schrödinger equations with combined nonlinearities. Precisely, we establish the mass threshold a¯ such that the mountain pass type normalized solution exists for the Sobolev critical/subcritical Schrödinger equation with combined mass critical and mass supercritical nonlinearities. We then show that a¯ is also a threshold of the limit behavior of the mountain pass type normalized solution of the Schrödinger equation with combined nonlinearities as the exponent of lower order term tending to the mass critical exponent. Among which, the results in the case that the mass small than the threshold a¯ give an affirmative answer to the conjecture raised by Soave.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
