scholarly journals Existence of One-Signed Solutions of Discrete Second-Order Periodic Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Ruyun Ma ◽  
Yanqiong Lu ◽  
Tianlan Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Periodic Boundary Value Problems ◽  
The Fixed Point Theorem

We prove the existence of one-signed periodic solutions of second-order nonlinear difference equation on a finite discrete segment with periodic boundary conditions by combining some properties of Green's function with the fixed-point theorem in cones.

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

scholarly journals Applications of Stieltjes Derivatives to Periodic Boundary Value Inclusions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2142
Author(s):  
Bianca Satco ◽  
George Smyrlis
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Solution Set ◽  
First Order

In the present paper, we are interested in studying first-order Stieltjes differential inclusions with periodic boundary conditions. Relying on recent results obtained by the authors in the single-valued case, the existence of regulated solutions is obtained via the multivalued Bohnenblust–Karlin fixed-point theorem and a result concerning the dependence on the data of the solution set is provided.

scholarly journals Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems

2021 ◽  
Vol 2 (1) ◽  
pp. 47-61
Author(s):  
Laila Hashtamand
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Fractional Order Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Stability Results

This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.

scholarly journals Positive Solutions of Three-Order Delayed Periodic Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Na Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Point Boundary ◽  
Periodic Boundary Value Problems ◽  
Existence Of Positive Solutions ◽  
Existence And Nonexistence ◽  
The Fixed Point Theorem

Our main purpose is to consider the existence of positive solutions for three-order two-point boundary value problem in the following form: u′′′(t)+ρ3u(t)=f(t,u(t-τ)),  0≤t≤2π,  u(i)(0)=u(i)(2π),  i=1,2,  u(t)=σ,  -τ≤t≤0, where σ,ρ, and τ are given constants satisfying τ∈(0,π/2). Some inequality conditions on ρ3u-f(t,u) guaranteeing the existence and nonexistence of positive solutions are presented. Our discussion is based on the fixed point theorem in cones.

scholarly journals Existence and Uniqueness of Positive Solution for Discrete Multipoint Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huili Ma ◽  
Huifang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: -Δ2u(t-1)=f(t,   u(t))+g(t,   u(t)),  t∈Z1,  T, subject to boundary conditions either u(0)-βΔu(0)=0, u(T+1)=αu(η) or Δu(0)=0, u(T+1)=αu(η), where 0<α<1,   β>0,  and   η∈Z2,T-1. The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration.

scholarly journals Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Francesca Faraci ◽  
Antonio Iannizzotto
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Accumulation Point ◽  
Second Order ◽  
Nontrivial Solutions ◽  
Nonautonomous Systems ◽  
Second Order Hamiltonian Systems

Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a functionu, and prove that the set of bifurcation points for the solutions of the system is notσ-compact. Then, we deal with a linear system depending on a real parameterλ>0and on a functionu, and prove that there existsλ∗such that the set of the functionsu, such that the system admits nontrivial solutions, contains an accumulation point.

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