scholarly journals Infinitely Many Solutions for a Generalized Periodic Boundary Value Problem without the Evenness Assumption

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaodong Gu ◽  
Mingliang Song
Keyword(s):  
Boundary Value Problem ◽  
Critical Point ◽  
Hamiltonian Systems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Periodic Boundary Value Problem ◽  
Infinitely Many Solutions ◽  
Critical Point Theorem ◽  
Second Order Hamiltonian Systems

In this paper, we investigate infinitely many solutions for the generalized periodic boundary value problem −x″−B0tx+B1tx=λ∇xVt,xa.e.t∈0,1,x1=Mx0,x′1=Nx′0 under the potential function Vt,x without the evenness assumption and obtain two new existence results by the multiple critical point theorem. Meanwhile, we give two corollaries for the periodic solutions of second-order Hamiltonian systems and an example that illustrates our results.

scholarly journals Nonmonotone impulse effects in second-order periodic boundary value problems

2004 ◽  
Vol 2004 (7) ◽  
pp. 577-590 ◽  
Author(s):  
Irena Rachůnková ◽  
Milan Tvrdý
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Lower Upper ◽  
Periodic Boundary Value Problems

We deal with the nonlinear impulsive periodic boundary value problemu″=f(t,u,u′),u(ti+)=Ji(u(ti)),u′(ti+)=Mi(u′(ti)),i=1,2,…,m,u(0)=u(T),u′(0)=u′(T). We establish the existence results which rely on the presence of a well-ordered pair(σ1,σ2)of lower/upper functions(σ1≤σ2 on [0,T])associated with the problem. In contrast to previous papers investigating such problems, the monotonicity of the impulse functionsJi,Miis not required here.

Periodic Problem Involving Quasilinear Differential Operator and Weak Singularity

2007 ◽  
Vol 7 (4) ◽  
Author(s):  
Alberto Cabada ◽  
Alexander Lomtatidze ◽  
Milan Tvrdý
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Problem ◽  
Existence Results ◽  
Periodic Boundary Value Problem ◽  
Weak Singularity ◽  
Strong Force ◽  
Space Singularity

AbstractWe study the singular periodic boundary value problem of the form(|u′|where 1 < p < ∞ and f ∈ Car([0, T] × (0,∞)) can have a repulsive space singularity at x = 0. Contrary to previous results by Mawhin and Jebelean, Liu Bing and Rachůnková and Tvrdý, we need not assume any strong force conditions. Our main existence results rely on a new antimaximum principle for periodic quasilinear periodic problem, which has an independent meaning.

scholarly journals Multiple positive solutions for periodic boundary value problem via variational methods

2008 ◽  
Vol 39 (2) ◽  
pp. 111-120 ◽  
Author(s):  
Yu Tian ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Periodic Boundary Value Problem ◽  
Multiple Positive Solutions

In this paper, we investigate the positive solutions of periodic boundary value problem. By using critical point theory the existence of multiple positive solutions is obtained.

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