Solution of the Boundary-Value Problem of Heat Conduction with Periodic Boundary Conditions

2020 ◽  
Vol 72 (2) ◽  
pp. 232-245
Author(s):  
F. Kanca ◽  
I. Baglan
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Conditions

scholarly journals Solvability of a fourth order boundary value problem with periodic boundary conditions

1988 ◽  
Vol 11 (2) ◽  
pp. 275-284
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Elastic Beam ◽  
Periodic Boundary Conditions ◽  
Uniqueness Of Solutions

Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.

Lyapunov-type inequality for an anti-periodic fractional boundary value problem

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Rui A. C. Ferreira
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Type Inequality ◽  
Periodic Boundary Conditions ◽  
Fractional Boundary Value Problem ◽  
Research Directions ◽  
Lyapunov Type Inequality

AbstractIn this note we present a Lyapunov-type inequality for a fractional boundary value problem with anti-periodic boundary conditions, that we show to be a generalization of a classical one. Moreover, we address the issue of further research directions for such type of inequalities.

scholarly journals Lyapunov Type Inequality for an Anti-Periodic Conformable Boundary Value Problem

2021 ◽  
Vol 45 (02) ◽  
pp. 289-298
Author(s):  
JAGAN MOHAN JONNALAGADDA ◽  
DEBANANDA BASUA ◽  
DIPAK KUMAR SATPATHI
Keyword(s):  
Lower Bound ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Type Inequality ◽  
Periodic Boundary Conditions ◽  
Lyapunov Type Inequality

In this article, we present a Lyapunov-type inequality for a conformable boundary value problem associated with anti-periodic boundary conditions. To demonstrate the applicability of established result, we obtain a lower bound on the eigenvalue of the corresponding eigenvalue problem.

scholarly journals Lyapunov-type inequality for a Riemann-Liouville type fractional boundary value problem with anti-periodic boundary conditions

2021 ◽  
Vol 40 (4) ◽  
pp. 873-884
Author(s):  
Jagan Mohan Jonnalagadda ◽  
Debananda Basua
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Type Inequality ◽  
Periodic Boundary Conditions ◽  
Fractional Boundary Value Problem ◽  
Liouville Type ◽  
Well Posed ◽  
Lyapunov Type Inequality

In this article, we establish a Lyapunov-type inequality for a two-point Riemann-Liouville type fractional boundary value problem associated with well-posed anti-periodic boundary conditions. As an application, we estimate a lower bound for the eigenvalue of the corresponding fractional eigenvalue problem.

scholarly journals Solvability of a fourth-order boundary value problem with periodic boundary conditions II

1991 ◽  
Vol 14 (1) ◽  
pp. 127-137 ◽  
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Special Case

Letf:[0,1]×R4→Rbe a function satisfying Caratheodory's conditions ande(x)∈L1[0,1]. This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problemd4udx4+f(x,u(x),u′(x),u″(x),u‴(x))=e(x),   0<x<1, withu(0)−u(1)=u′(0)−u′(1)=u″(0)-u″(1)=u‴(0)-u‴(1)=0. This problem was studied earlier by the author in the special case whenfwas of the formf(x,u(x)), i.e., independent ofu′(x),u″(x),u‴(x). It turns out that the earlier methods do not apply in this general case. The conditions need to be related to both of the linear eigenvalue problemsd4udx4=λ4uandd4udx4=−λ2d2udx2with periodic boundary conditions.

scholarly journals Quasilinearization for the periodic boundary value problem for systems of impulsive differential equations

2006 ◽  
Vol 2006 ◽  
pp. 1-25 ◽  
Author(s):  
S. G. Hristova ◽  
A. S. Vatsala
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Periodic Boundary Conditions ◽  
Periodic Boundary Value Problem

The method of generalized quasilinearization for the system of nonlinear impulsive differential equations with periodic boundary conditions is studied. As a byproduct, the result for the system without impulses can be obtained, which is a new result as well.

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