scholarly journals The Existence and Uniqueness of Positive Solutions of an Ordinary Differential Equation with a Nonlocal Conditions

2021 ◽  
Vol 1900 (1) ◽  
pp. 012010
Author(s):  
E O Bin-taher
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Nonlocal Conditions

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

2020 ◽  
Vol 27 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Adjoint Problem ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Order Linear ◽  
Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

scholarly journals A blow-up dichotomy for semilinear fractional heat equations

2020 ◽  
Author(s):  
Robert Laister ◽  
Mikołaj Sierżęga
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Positive Solutions ◽  
Finite Time ◽  
Blow Up ◽  
Heat Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Whole Space ◽  
Necessary And Sufficient

Abstract We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive solutions to become unbounded in finite time. Moreover, we show that this condition is equivalent to blow-up of all positive solutions of a closely-related scalar ordinary differential equation.

scholarly journals Uniqueness of Positive Solutions for a Perturbed Fractional Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Chen Yang ◽  
Jieming Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Point Boundary ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We are concerned with the existence and uniqueness of positive solutions for the following nonlinear perturbed fractional two-point boundary value problem:D0+αu(t)+f(t,u,u',…,u(n-2))+g(t)=0, 0<t<1, n-1<α≤n, n≥2,u(0)=u'(0)=⋯=u(n-2)(0)=u(n-2)(1)=0, whereD0+αis the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem of generalized concave operators. An example is given to illustrate the main result.

scholarly journals Positive Solutions of a Nonlinear Parabolic Partial Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Chengbo Zhai ◽  
Shunyong Li
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Monotone Operators ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Parabolic ◽  
Mixed Monotone Operators

We deal with the existence and uniqueness of positive solutions to a class of nonlinear parabolic partial differential equations, by using some fixed point theorems for mixed monotone operators with perturbation.

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