scholarly journals Multiple Solutions of Boundary Value Problems fornth-Order Singular Nonlinear Integrodifferential Equations in Abstract Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Yanlai Chen ◽  
Tingqiu Cao ◽  
Baoxia Qin
Keyword(s):  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Third Order ◽  
The Fixed Point Theorem ◽  
Abstract Spaces ◽  
Cone Expansion And Compression

The authors discuss multiple solutions for thenth-order singular boundary value problems of nonlinear integrodifferential equations in Banach spaces by means of the fixed point theorem of cone expansion and compression. An example for infinite system of scalar third-order singular nonlinear integrodifferential equations is offered.

scholarly journals Numerical solutions for a class of singular boundary value problems arising in the theory of epitaxial growth

2020 ◽  
Vol 37 (7) ◽  
pp. 2539-2560 ◽  
Author(s):  
Amit K. Verma ◽  
Biswajit Pandit ◽  
Carlos Escudero
Keyword(s):  
Boundary Value Problems ◽  
Numerical Method ◽  
Epitaxial Growth ◽  
Multiple Solutions ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Content Type ◽  
Nonexistence Of Solutions

Purpose This paper aims to apply an iterative numerical method to find the numerical solution of the nonlinear non-self-adjoint singular boundary value problems that arises in the theory of epitaxial growth. Design/methodology/approach The proposed problem has multiple solutions and it is singular too; so not every technique can capture all the solutions. This study proposes to use variational iterative numerical method and compute both the solutions. The computed solutions are very close to the exact result. Findings It turns out that the existence or nonexistence of numerical solutions fully depends on the value of a parameter. The authors show that numerical solutions exist for small positive values of this parameter. For large positive values of the parameter, they find nonexistence of solutions. They also observe existence of solutions for negative values of the parameter and determine the range of parameter values which separates existence and nonexistence of solutions. This parameter has a clear physical meaning, as it describes the rate at which new material is deposited onto the system. This fact allows interpreting the physical significance of the results. Originality/value The authors could capture both the solutions and got accurate estimation of the parameter. This method will be a great tool to handle such types of nonlinear non-self-adjoint equations that have multiple solutions in engineering and mathematical sciences. The results in this paper will have an impact on the understanding of theoretical models of epitaxial growth in near future.

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