Riemann-Hilbert approach to TD equation with nonzero boundary condition

2018 ◽  
Vol 13 (5) ◽  
pp. 1245-1265 ◽  
Author(s):  
Junyi Zhu ◽  
Linlin Wang ◽  
Xianguo Geng
Keyword(s):  
Boundary Condition ◽  
Nonzero Boundary ◽  
Nonzero Boundary Condition

scholarly journals Classical and Impulse Stochastic Control on the Optimization of Dividends with Residual Capital at Bankruptcy

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Peimin Chen ◽  
Bo Li
Keyword(s):  
Boundary Condition ◽  
Variational Inequalities ◽  
Stochastic Control ◽  
Optimization Problem ◽  
Value Function ◽  
The State ◽  
Tax Rate ◽  
Nonzero Boundary ◽  
The Value Function ◽  
Nonzero Boundary Condition

In this paper, we consider the optimization problem of dividends for the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, while accounting for the tax rate and transaction cost for dividend payout. Maximization of both expected total discounted dividends before bankruptcy and expected discounted returned money at the state of terminal bankruptcy becomes a mixed classical-impulse stochastic control problem. In order to solve this problem, we reduce it to quasi-variational inequalities with a nonzero boundary condition. We explicitly construct and verify solutions of these inequalities and present the value function together with the optimal policy.

scholarly journals Soliton solutions to a (2+1)-dimensional nonlocal NLS equation

2021 ◽  
Author(s):  
Qiaofeng Huang ◽  
Chenzhi Ruan ◽  
Jiaxing Huang
Keyword(s):  
Boundary Condition ◽  
Soliton Solutions ◽  
Kp Hierarchy ◽  
Nls Equation ◽  
Bilinear Method ◽  
Kp Hierarchy Reduction Method ◽  
Back Ground ◽  
Nonzero Boundary ◽  
Non Local ◽  
N Gram

Abstract In this paper, applying the Hirota’s bilinear method and the KP hierarchy reduction method, we obtain the general soliton solutions in the forms of N × N Gram-type determinants to a (2+1)-dimensional non-local nonlinear Schrodinger equation with time reversal under zero and nonzero boundary conditions. The general bright soliton solutions with zero boundary condition are derived via the tau functions of two-component KP hierarchy. Under nonzero boundary condition, we first construct general soliton solutions on periodic back-ground, when N is odd. Furthermore, we discuss typical dynamics of solutions analytically, and graphically.

One-Dimensional Fin-Tip Boundary Condition Correction II

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan
Keyword(s):  
Boundary Condition ◽  
One Dimensional

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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