scholarly journals Method of Lower and Upper Solutions for Elliptic Systems with Nonlinear Boundary Condition and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ruyun Ma ◽  
Ruipeng Chen ◽  
Yanqiong Lu
Keyword(s):  
Nonlinear Boundary ◽  
System Modeling ◽  
Principal Eigenvalue ◽  
Age Groups ◽  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Nonlinear Boundary Conditions ◽  
Lower And Upper Solutions ◽  
Adult Age ◽  
Adult Model

We develop the method of lower and upper solutions for a class of elliptic systems with nonlinear boundary conditions. As its application, an elliptic system modeling a population divided into juvenile and adult age groups is studied, and we find sufficient conditions in terms of the principal eigenvalue of the corresponding linearized system, to guarantee the existence of coexistence states of the above juvenile-adult model.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

scholarly journals On a System Modelling a Population with Two Age Groups

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hongliang Gao ◽  
Ruyun Ma
Keyword(s):  
Differential Equations ◽  
Principal Eigenvalue ◽  
Linear Part ◽  
Age Groups ◽  
System Modelling ◽  
Adult Age ◽  
First Order ◽  
Existence And Nonexistence ◽  
Linearized System ◽  
Two Age Groups

A system of first order ordinary differential equations describing a population divided into juvenile and adult age groups is studied. The system is not cooperative but its linear part is, and this makes it possible to establish the existence and nonexistence results of positive solutions for the system in terms of the principal eigenvalue of the corresponding linearized system.

scholarly journals Systems of differential equations with fully nonlinear boundary conditions

1997 ◽  
Vol 56 (2) ◽  
pp. 197-208 ◽  
Author(s):  
H.B. Thompson
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Neumann Boundary ◽  
Nonlinear Boundary Conditions ◽  
Fully Nonlinear ◽  
Systems Of Differential Equations ◽  
Special Cases

We give sufficient conditions involving f, g and ω in order that systems of differential equations of the form y″ = f(x, y, y′), x in [0, 1] with fully nonlinear boundary conditions of the form g((y(0), y(1)), (y′(0), y′(1))) = 0 have solutions y with (x, y) in . We use Schauder degree theory in a novel space. Well known existence results for the Picard, the periodic and the Neumann boundary conditions follow as special cases of our results.

scholarly journals On the Parametrization of Caputo-Type Fractional Differential Equations with Two-Point Nonlinear Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 707 ◽  
Author(s):  
Nazım I. Mahmudov ◽  
Sedef Emin ◽  
Sameer Bawanah
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Nonlinear Boundary ◽  
Sufficient Conditions ◽  
Nonlinear Boundary Conditions ◽  
Successive Approximations ◽  
Limit Function ◽  
Fractional Differential ◽  
Linear Restrictions

In this paper, we offer a new approach of investigation and approximation of solutions of Caputo-type fractional differential equations under nonlinear boundary conditions. By using an appropriate parametrization technique, the original problem with nonlinear boundary conditions is reduced to the equivalent parametrized boundary-value problem with linear restrictions. To study the transformed problem, we construct a numerical-analytic scheme which is successful in relation to different types of two-point and multipoint linear boundary and nonlinear boundary conditions. Moreover, we give sufficient conditions of the uniform convergence of the successive approximations. Also, it is indicated that these successive approximations uniformly converge to a parametrized limit function and state the relationship of this limit function and exact solution. Finally, an example is presented to illustrate the theory.

scholarly journals POSITIVE SOLUTIONS OF HIGHER-ORDER BOUNDARY-VALUE PROBLEMS

2005 ◽  
Vol 48 (2) ◽  
pp. 445-464 ◽  
Author(s):  
Lingju Kong ◽  
Qingkai Kong
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Boundary Conditions ◽  
Existence Of Positive Solutions ◽  
Eigenvalue Parameter ◽  
Even Order

AbstractWe consider a class of even-order boundary-value problems with nonlinear boundary conditions and an eigenvalue parameter $\lambda$ in the equations. Sufficient conditions are obtained for the existence and non-existence of positive solutions of the problems for different values of $\lambda$.

scholarly journals Analysis of a Nonlinear ψ-Hilfer Fractional Integro-Differential Equation Describing Cantilever Beam Model with Nonlinear Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 177
Author(s):  
Kanoktip Kotsamran ◽  
Weerawat Sudsutad ◽  
Chatthai Thaiprayoon ◽  
Jutarat Kongson ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Point Theorem ◽  
Nonlinear Boundary ◽  
Sufficient Conditions ◽  
Nonlinear Boundary Conditions ◽  
Beam Model ◽  
Uniqueness Of Solutions

In this paper, we establish sufficient conditions to approve the existence and uniqueness of solutions of a nonlinear implicit ψ-Hilfer fractional boundary value problem of the cantilever beam model with nonlinear boundary conditions. By using Banach’s fixed point theorem, the uniqueness result is proved. Meanwhile, the existence result is obtained by applying the fixed point theorem of Schaefer. Apart from this, we utilize the arguments related to the nonlinear functional analysis technique to analyze a variety of Ulam’s stability of the proposed problem. Finally, three numerical examples are presented to indicate the effectiveness of our results.

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