On nonlinear boundary value problem corresponding to $N$-dimensional inverse spectral problem
| Autor: | Y.Sh. Ilyasov, N. F. Valeev |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
FOS: Physical sciences
Inverse 01 natural sciences Stability (probability) Schrödinger equation Mathematics - Spectral Theory symbols.namesake Mathematics - Analysis of PDEs FOS: Mathematics Uniqueness 0101 mathematics Spectral Theory (math.SP) Mathematical Physics Mathematics N dimensional Applied Mathematics 010102 general mathematics Mathematical analysis Mathematical Physics (math-ph) 010101 applied mathematics 35P30 35R30 35J65 35J10 35J60 Exact solutions in general relativity symbols Inverse optimization Nonlinear boundary value problem Analysis Analysis of PDEs (math.AP) |
| Popis: | We establish a relationship between an inverse optimization spectral problem for N-dimensional Schr\"odinger equation $ -\Delta \psi+q\psi=\lambda \psi $ and a solution of the nonlinear boundary value problem $-\Delta u+q_0 u=\lambda u- u^{\gamma-1},~~u>0,~~ u|_{\partial \Omega}=0$. Using this relationship, we find an exact solution for the inverse optimization spectral problem, investigate its stability and obtain new results on the existence and uniqueness of the solution for the nonlinear boundary value problem. Comment: 11 pages |
| Databáze: | OpenAIRE |
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