scholarly journals Nontrivial Solutions for the 2 n th Lidstone Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yaohong Li ◽  
Jiafa Xu ◽  
Yongli Zan
Keyword(s):  
Linear Operator ◽  
Boundary Value Problem ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Nontrivial Solutions

In this paper, we study the existence of nontrivial solutions for the 2 n th Lidstone boundary value problem with a sign-changing nonlinearity. Under some conditions involving the eigenvalues of a linear operator, we use the topological degree theory to obtain our main results.

scholarly journals Nontrivial Solutions for a System of Second-Order Discrete Boundary Value Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hua Su ◽  
Yongqing Wang ◽  
Jiafa Xu
Keyword(s):  
Linear Operator ◽  
Boundary Value Problems ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Second Order ◽  
Topological Degree Theory ◽  
Nontrivial Solutions

In this work, we shall study the existence of nontrivial solutions for a system of second-order discrete boundary value problems. Under some conditions concerning the eigenvalues of relevant linear operator, we use the topological degree theory to obtain our main results.

scholarly journals Nontrivial Solutions for a Boundary Value Problem of nth-Order Impulsive Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jiafa Xu ◽  
Zhongli Wei
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Impulsive Differential Equation ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Degree Theory ◽  
Impulsive Effects ◽  
Nontrivial Solutions

We study the existence of nontrivial solutions for nth-order boundary value problem with impulsive effects. We utilize Leray-Schauder degree theory to establish our main results. Furthermore, our nonlinear term f is allowed to grow superlinearly and sublinearly.

scholarly journals Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yansheng Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This paper is concerned with the existence of positive solutions for a class of boundary value problems of fractional differential equations with parameter. The main tools used here are bifurcation techniques and topological degree theory. Finally, an example is worked out to demonstrate the main result.

scholarly journals Bifurcation from Interval and Positive Solutions of a Nonlinear Second-Order Dynamic Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hua Luo
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scale ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Degree Theory ◽  
Second Order ◽  
Topological Degree Theory ◽  
Bifurcation From Interval

Let𝕋be a time scale with0,T∈𝕋. We give a global description of the branches of positive solutions to the nonlinear boundary value problem of second-order dynamic equation on a time scale𝕋,uΔΔ(t)+f(t,uσ(t))=0,  t∈[0,T]𝕋,  u(0)=u(σ2(T))=0, which is not necessarily linearizable. Our approaches are based on topological degree theory and global bifurcation techniques.

scholarly journals Topological essentiality and differential inclusions

1992 ◽  
Vol 45 (2) ◽  
pp. 177-193 ◽  
Author(s):  
Lech Gorniewicz ◽  
Miroslaw Slosarski
Keyword(s):  
Boundary Value Problems ◽  
Large Class ◽  
Differential Inclusion ◽  
Topological Degree ◽  
Differential Inclusions ◽  
Boundary Value ◽  
Degree Theory ◽  
Multivalued Mappings ◽  
Topological Degree Theory ◽  
Lower Semi

In the present paper a concept of topological essentiality for a large class of multivalued mappings is introduced. This concept is strictly related to the Leray-Schauder topological degree theory but is simpler and also more general. Applying the above concept to boundary value problems for differential inclusion with both upper semi-continuous and lower semi-continuous right hand sides, several new results are obtained.

scholarly journals A Boundary Value Problem for Noninsulated Magnetic Regime in a Vacuum Diode

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 617
Author(s):  
Edixon M. Rojas ◽  
Nikolai A. Sidorov ◽  
Aleksandr V. Sinitsyn
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Boundary Value ◽  
Singular System ◽  
Degree Theory ◽  
Fredholm Integral Equations ◽  
Topological Degree Theory ◽  
System Of Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Nonlinear Singular System

In this paper, we study the stationary boundary value problem derived from the magnetic (non) insulated regime on a plane diode. Our main goal is to prove the existence of non-negative solutions for that nonlinear singular system of second-order ordinary differential equations. To attain such a goal, we reduce the boundary value problem to a singular system of coupled nonlinear Fredholm integral equations, then we analyze its solvability through the existence of fixed points for the related operators. This system of integral equations is studied by means of Leray-Schauder’s topological degree theory.

scholarly journals Solvability for a Fractional Order Three-Point Boundary Value System at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Zigen Ouyang ◽  
Hongliang Liu
Keyword(s):  
Integral Equation ◽  
Fractional Order ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
New Method ◽  
Point Boundary ◽  
Topological Degree Theory ◽  
Value System ◽  
At Resonance

A class of fractional order three-point boundary value system with resonance is investigated in this paper. Using some techniques of inequalities, a completely new method is incorporated. We transform the problem into an integral equation with a pair of undetermined parameters. The topological degree theory is applied to determine the particular value of the parameters so that the system has a solution.

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