scholarly journals On nonlinear boundary value problems with deviating arguments and discontinuous right hand side

1993 ◽  
Vol 6 (1) ◽  
pp. 83-91
Author(s):  
B. C. Dhage ◽  
S. Heikkilä
Keyword(s):  
Differential Equation ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
Right Hand ◽  
Nonlinear Boundary Value ◽  
The Right ◽  
Generalized Iteration

In this paper we shall study the existence of the extremal solutions of a nonlinear boundary value problem of a second order differential equation with general Dirichlet/Neumann form boundary conditions. The right hand side of the differential equation is assumed to contain a deviating argument, and it is allowed to possess discontinuities in all the variables. The proof is based on a generalized iteration method.

scholarly journals Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Quasilinearization Method ◽  
Nonlinear Boundary Value Problems ◽  
Wavelet Galerkin Method ◽  
Nonlinear Boundary Value ◽  
Quasilinearization Technique

A numerical method is proposed by wavelet-Galerkin and quasilinearization approach for nonlinear boundary value problems. Quasilinearization technique is applied to linearize the nonlinear differential equation and then wavelet-Galerkin method is implemented to linearized differential equations. In each iteration of quasilinearization technique, solution is updated by wavelet-Galerkin method. In order to demonstrate the applicability of proposed method, we consider the various nonlinear boundary value problems.

scholarly journals On the extremal solution for a nonlinear boundary value problems of fractional p-Laplacian differential equation

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3771-3778 ◽  
Author(s):  
Youzheng Ding ◽  
Zhongli Wei
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Extremal Solution ◽  
Lower And Upper Solutions ◽  
Laplacian Operator ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

This paper is concerned with the existence and uniqueness of extremal solution for a nonlinear boundary value problems of fractional differential equation involving Riemann-Liouville derivative and p-Laplacian operator. By applying monotone iterative technique and lower and upper solutions method, we obtain sufficient conditions for the existence and uniqueness of extremal solution and construct the sequences of iteration to approximate it. The paper extends the applications of lower and upper solutions method and obtains some new results.

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