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 Existence results for a sublinear second order Dirichlet boundary value problem on the half-line

2020 ◽  
Vol 40 (5) ◽  
pp. 537-548
Author(s):  
Dahmane Bouafia ◽  
Toufik Moussaoui
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Half Line ◽  
Dirichlet Boundary Value Problem ◽  
Nontrivial Solutions

In this paper we study the existence of nontrivial solutions for a boundary value problem on the half-line, where the nonlinear term is sublinear, by using Ekeland's variational principle and critical point theory.

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 of a Fully Fourth-Order Periodic Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Haitong Li ◽  
Minghe Pei ◽  
Libo Wang
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Periodic Boundary Value Problem ◽  
Coincidence Degree Theory ◽  
Nontrivial Solutions ◽  
Carathéodory Conditions

We investigate the solvability of a fully fourth-order periodic boundary value problem of the formx(4)=f(t,x,x′,x′′,x′′′),  x(i)(0)=x(i)(T),      i=0,1,2,3,wheref:[0,T]×R4→Rsatisfies Carathéodory conditions. By using the coincidence degree theory, the existence of nontrivial solutions is obtained. Meanwhile, as applications, some examples are given to illustrate our results.

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