scholarly journals Existence and Uniqueness of Solutions to a Nonlinear Boundary Value Problem

1968 ◽  
Vol 18 (6) ◽  
pp. 585-586
Author(s):  
Paul Waltman
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Nonlinear Boundary Value

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.

scholarly journals Existence and uniqueness of solutions for a class of fractional nonlinear boundary value problems under mild assumptions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Imed Bachar ◽  
Habib Mâagli ◽  
Hassan Eltayeb
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Continuous Solution ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Of Solutions ◽  
Nonlinear Boundary Value ◽  
Appl Math

AbstractWe deal with the following Riemann–Liouville fractional nonlinear boundary value problem: $$ \textstyle\begin{cases} \mathcal{D}^{\alpha }v(x)+f(x,v(x))=0, & 2< \alpha \leq 3, x\in (0,1), \\ v(0)=v^{\prime }(0)=v(1)=0. \end{cases} $$ { D α v ( x ) + f ( x , v ( x ) ) = 0 , 2 < α ≤ 3 , x ∈ ( 0 , 1 ) , v ( 0 ) = v ′ ( 0 ) = v ( 1 ) = 0 . Under mild assumptions, we prove the existence of a unique continuous solution v to this problem satisfying $$ \bigl\vert v(x) \bigr\vert \leq cx^{\alpha -1}(1-x)\quad\text{for all }x \in [ 0,1]\text{ and some }c>0. $$ | v ( x ) | ≤ c x α − 1 ( 1 − x ) for all  x ∈ [ 0 , 1 ]  and some  c > 0 . Our results improve those obtained by Zou and He (Appl. Math. Lett. 74:68–73, 2017).

scholarly journals Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. M. Matar ◽  
M. I. Abbas ◽  
J. Alzabut ◽  
M. K. A. Kaabar ◽  
S. Etemad ◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives

AbstractA newly proposed p-Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives. The existence and uniqueness of solutions are fully investigated for this problem using some fixed point theorems such as Banach and Schauder. This work is supported with an example to apply all obtained new results and validate their applicability.

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.

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