scholarly journals Boundary Value Problems forq-Difference Inclusions

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Nonseparated Boundary Conditions ◽  
Difference Inclusions ◽  
The Right

We investigate the existence of solutions for a class of second-orderq-difference inclusions with nonseparated boundary conditions. By using suitable fixed-point theorems, we study the cases when the right-hand side of the inclusions has convex as well as nonconvex values.

scholarly journals Some Results on Fractional m-Point Boundary Value Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Huijuan Zhu ◽  
Baozhi Han ◽  
Jun Shen
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Lyapunov’S Inequality ◽  
The Given ◽  
Stability Results

In this paper, we will apply some fixed-point theorems to discuss the existence of solutions for fractional m-point boundary value problems D 0 + q u ″ t = h t f u t , t ∈ 0 , 1 , 1 < q ≤ 2 , u ′ 0 = u ″ 0 = u 1 = 0 , u ″ 1 − ∑ i = 1 m − 2 α i u ‴ ξ i = 0 . In addition, we also present Lyapunov’s inequality and Ulam-Hyers stability results for the given m-point boundary value problems.

scholarly journals Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dionicio Pastor Dallos Santos
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Nonlinear Boundary Value Problems

We study the existence of solutions for nonlinear boundary value problemsφu′′=ft,u,u′,  lu,u′=0, wherel(u,u′)=0denotes the boundary conditions on a compact interval0,T,φis a homeomorphism such thatφ(0)=0, andf:0,T×R×R→Ris a continuous function. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree is used.

scholarly journals On the Second-Order Quantum (p,q)-Difference Equations with Separated Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chanon Promsakon ◽  
Nattapong Kamsrisuk ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Uniqueness Of Solutions ◽  
Separated Boundary Conditions

In this paper, we investigate the existence and uniqueness of solutions for a boundary value problem for second-order quantum (p,q)-difference equations with separated boundary conditions, by using classical fixed point theorems. Examples illustrating the main results are also presented.

scholarly journals Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Yanping Guo ◽  
Jiehua Zhang ◽  
Yude Ji
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Triple Positive Solutions

By using a new fixed-point theorem introduced by Avery and Peterson (2001), we obtain sufficient conditions for the existence of at least three positive solutions for the equationΔ2x(k−1)+q(k)f(k,x(k),Δx(k))=0, fork∈{1,2,…,n−1}, subject to the following two boundary conditions:x(0)=x(n)=0orx(0)=Δx(n−1)=0, wheren≥3.

scholarly journals Existence of Nontrivial Solutions for Some Second-Order Multipoint Boundary Value Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Hongyu Li ◽  
Junting Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Lattice Structure ◽  
Boundary Value ◽  
Second Order ◽  
Negative Solution ◽  
Nontrivial Solutions ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

By using fixed point theorems with lattice structure, the existence of negative solution and sign-changing solution for some second-order multipoint boundary value problems is obtained.

scholarly journals Some fixed point results for $ \alpha $-admissible extended $ \mathcal{Z} $-contraction mappings in extended rectangular $ b $-metric spaces

2021 ◽  
Vol 7 (3) ◽  
pp. 3701-3718
Author(s):  
Yan Sun ◽  
◽  
Xiao-lan Liu ◽  
Jia Deng ◽  
Mi Zhou ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Contraction Mappings

<abstract><p>In this paper, we introduce $ \alpha $-admissible extended $ \mathcal{Z} $-contraction in the extended rectangular $ b $-metric spaces, then we provide some other conditions in Theorem 3.1, which are different from that in Chifu et al. <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, and obtain the existence and uniqueness of fixed point in such spaces. Moreover, some examples are given to show the validity of our main theorems, and we give some corollaries related to our main results. As an application, we apply our main results to solve the existence of solutions for a class of boundary value problems of second order ordinary differential equations.</p></abstract>

scholarly journals A new result of Presic type theorems with applications to second order boundary value problems

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2257-2266
Author(s):  
Ishak Altun ◽  
Muhammad Qasim ◽  
Murat Olgun
Keyword(s):  
Fixed Point ◽  
Theoretical Result ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Second Order ◽  
Point Boundary ◽  
Special Case

In this paper, taking into account the recent contractive technique we present a new result of Presic type fixed point theorems. Then, we provide a comparative example to put forth the validity of our theoretical result. Finally, considering a special case of the main theorem, we give some existence results for the second order two point boundary value problems.

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