Uniqueness and non-uniqueness of solutions of the boundary value problems of the heat equation

2015 ◽  
Author(s):  
Meiramkul M. Amangaliyeva ◽  
Muvasharkhan T. Jenaliyev ◽  
Minzilya T. Kosmakova ◽  
Murat I. Ramazanov
Keyword(s):  
Heat Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Uniqueness Of Solutions

scholarly journals Existence and Uniqueness of Solutions to Third-Order Boundary Value Problems

2021 ◽  
Vol 22 (2) ◽  
pp. 221-240
Author(s):  
S. S. Almuthaybiri ◽  
J. M. Jonnalagadda ◽  
C. C. Tisdell
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Fixed Point Methods ◽  
Bounded Sets

The purpose of this research is to connect fixed point methods with certain third-order boundary value problems in new and interesting ways. Our strategy involves an analysis of the problem under consideration within closed and bounded sets. We develop sufficient conditions under which the associated mappings will be contractive and invariant in these sets, which generates new advances concerning the existence, uniqueness and approximation of solutions.

scholarly journals Hilfer-Hadamard Nonlocal Integro-Multipoint Fractional Boundary Value Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Chanon Promsakon ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
New Class ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle

This paper is concerned with the existence and uniqueness of solutions for a new class of boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented with nonlocal integro-multipoint boundary conditions. The existence of a unique solution is obtained via Banach contraction mapping principle, while the existence results are established by applying Schaefer and Krasnoselskii fixed point theorems as well as Leray-Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

Quasilinearization and boundary value problems at resonance

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Kareem Alanazi ◽  
Meshal Alshammari ◽  
Paul Eloe
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Approximate Solutions ◽  
Monotonicity Condition ◽  
Uniqueness Of Solutions ◽  
Shift Method ◽  
At Resonance ◽  
Problem At Resonance

Abstract A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

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