| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
In this research, I have investigated minimization problems related with the stabilizing effect for standing waves caused by non-local interactions. Especially, I have studied the solution structure (uniqueness, multiplicity and asymptotic profile) of the stationary problem of a quasilinear Schroedinger equation which is derived as a limit equation. One of the main results of my research is to show the uniqueness and the non-degeneracy of ground state solutions for a whole range of parameters. Moreover, I have studied the asymptotic behavior of solutions when the nonlinear term has the Sobolev critical growth. My result completely reveals how the parameter dependence of the asymptotic profiles of solutions changes with respect to the nonlinear exponent.
I have also performed the stability analysis of standing waves for the Schroedinger-Maxwell system, and investigated several other physical models.
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