A modified Schrödinger-type identity: uniqueness of solutions for singular boundary value problem for the Schrödinger equation

Author:

He Hongjun,Pang Zhifeng

Abstract

Abstract This paper is devoted to modifying the Schrödinger-type identity related to singular boundary value problem in (Zhang et al. in Bound. Value Probl. 2018:135, 2018). We also present some mathematical consequences of the method, including a stability result. The main technical tools used to develop the mathematical analysis are local and global bifurcation, monotonicity techniques, fixed point theory in b-metric spaces in (Liu et al. in Bull. Aust. Math. Soc. 94(1):121–130, 2016) and the maximum principle approach with respect to the Schrödinger operator in (Fan et al. in Math. Appl. 31(1):42–48, 2018). As an application, the uniqueness of solutions for singular boundary value problem for the Schrödinger equation is proved.

Publisher

Springer Science and Business Media LLC

Subject

Algebra and Number Theory,Analysis

Reference32 articles.

1. Zhang, X., Liu, D., Yan, Z., Zhao, G., Yuan, Y.: Schrödinger-type identity for Schrödinger free boundary problems. Bound. Value Probl. 2018, 135 (2018)

2. Liu, F., Chen, T., Wu, H.: A note on the endpoint regularity of the Hardy–Littlewood maximal functions. Bull. Aust. Math. Soc. 94(1), 121–130 (2016)

3. Fan, J., He, F., Ren, K.: Fixed point theorem with Jachymski function in dislocated quasi-metric spaces. Math. Appl. 31(1), 42–48 (2018)

4. Gilardi, G.: A new approach to evolution free boundary problems. Commun. Partial Differ. Equ. 4, 1099–1123 (1979)

5. Rossi, J.D.: The blow-up rate for a semilinear parabolic equation with a nonlinear boundary condition. Acta Math. Univ. Comen. 67, 343–350 (1998)

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