Existence and Uniqueness of a Weak Solution of the Nonlinear Boundary Value Problem

2018 ◽  
pp. 45-53
Author(s):  
Lutz Angermann ◽  
Vasyl V. Yatsyk
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Nonlinear Boundary Value

scholarly journals On the existence of equilibrium states of an elastic beam on a nonlinear foundation

1993 ◽  
Vol 16 (1) ◽  
pp. 193-198
Author(s):  
M. B. M. Elgindi ◽  
D. H. Y. Yen
Keyword(s):  
Boundary Value Problem ◽  
Axial Compression ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Nonlinear Eigenvalue Problem ◽  
Boundary Value ◽  
Elastic Beam ◽  
Equilibrium States ◽  
Nonlinear Boundary Value Problem ◽  
Nonlinear Boundary Value

This paper concerns the existence and uniqueness of equilibrium states of a beam-column with hinged ends which is acted upon by axial compression and lateral forces and is in contact with a semi-infinite medium acting as a foundation. The problem is formulated as a fourth-order nonlinear boundary value problem in which the source of the nonlinearity comes from the lateral constraint (the foundation). Treating the equation of equilibrium as a nonlinear eigenvalue problem we prove the existence of a pair of eigenvalue/eigenfunction for each arbitrary prescribed energy level. Treating the equilibrium equation as a nonlinear boundary value problem we prove the existence and uniqueness of solution for a certain range of the acting axial compression force.

scholarly journals On the existence and uniqueness of solutions to a singular nonlinear boundary value problem arising in isothermal autocatalytic chemical kinetics

1993 ◽  
Vol 36 (3) ◽  
pp. 479-500 ◽  
Author(s):  
D. J. Needham ◽  
A. C. King
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Solution ◽  
Chemical Kinetics ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Small Time ◽  
Nonlinear Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Nonlinear Boundary Value

In this paper we consider the questions of existence and uniqueness of solutions to a singular, nonlinear boundary value problem arising from a model problem in isothermal autocatalytical chemical kinetics. The boundary value problem occurs in the construction of a small time asymptotic solution to an initial-boundary value problem (King and Needham [14]), and existence and uniqueness for the boundary value problem are required for consistency of this formal asymptotic solution.

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