scholarly journals Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions

2006 ◽  
Vol 13 (2) ◽  
pp. 215-228
Author(s):  
Abdelkader Belarbi ◽  
Mouffak Benchohra ◽  
Bapurao C. Dhage
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Existence Theory ◽  
Nonlinear Boundary Value Problems ◽  
Integral Boundary ◽  
Carathéodory Conditions ◽  
Nonlinear Boundary Value

Abstract In this paper, the existence of solutions and extremal solutions for a second order perturbed nonlinear boundary value problem with integral boundary conditions is proved under the mixed generalized Lipschitz and Carathéodory conditions.

Solvability for nonlocal boundary value problems with generalized 𝑝-Laplacian on an unbounded domain

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Marek Matyjasik ◽  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Nonlinear Boundary Value Problems ◽  
Integral Boundary ◽  
Positive Half

Abstract This paper is devoted to the existence of solutions for a class of nonlinear boundary value problems with integral boundary conditions and generalized 𝑝-Laplacian on the positive half-line. We establish sufficient conditions to guarantee the existence of solutions in a special function space by using Leray–Schauder-type arguments. Examples are also given to illustrate the main results.

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.

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