Some Liouville theorems for Hénon type equations in half-space with nonlinear boundary value conditions and finite Morse indices

2020 ◽  
Vol 10 (4) ◽  
Author(s):  
Belgacem Rahal
Keyword(s):  
Half Space ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Liouville Theorems ◽  
Nonlinear Boundary Value ◽  
Morse Indices

Solving nonlinear boundary value problems by a boundary shape function method and a splitting and linearizing method

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Chein-Shan Liu ◽  
Essam R. El-Zahar ◽  
Chih-Wen Chang
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Shape Function ◽  
Boundary Value ◽  
Linear Equations ◽  
Accurate Solution ◽  
Iteration Step ◽  
Nonlinear Boundary Value Problems ◽  
Boundary Shape ◽  
Nonlinear Boundary Value

Abstract In the paper, we develop two novel iterative methods to determine the solution of a second-order nonlinear boundary value problem (BVP), which precisely satisfies the specified non-separable boundary conditions by taking advantage of the property of the corresponding boundary shape function (BSF). The first method based on the BSF can exactly transform the BVP to an initial value problem for the new variable with two given initial values, while two unknown terminal values are determined iteratively. By using the BSF in the second method, we derive the fractional powers exponential functions as the bases, which automatically satisfy the boundary conditions. A new splitting and linearizing technique is used to transform the nonlinear BVP into linear equations at each iteration step, which are solved to determine the expansion coefficients and then the solution is available. Upon adopting those two novel methods very accurate solution for the nonlinear BVP with non-separable boundary conditions can be found quickly. Several numerical examples are solved to assess the efficiency and accuracy of the proposed iterative algorithms, which are compared to the shooting method.

Sign in / Sign up

Export Citation Format

Share Document