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result(s) for
"34B10"
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An efficient iterative procedure in hyperbolic space and application to non-linear delay integral equation
In the context of hyperbolic spaces, our study presents a novel iterative approach for approximating common fixed points satisfying general contractive condition involving a pair of mappings with weak compatibility. Also, we notice that our iterative procedure approximates to a point of coincidence if the weak compatibility condition is violated. We provide theorems to demonstrate the
Δ
-
convergence, stability, and efficiency of this iteration process. Additionally, we provided some immediate corollaries that involve mappings with contractive condition, instead of general contractive condition. Furthermore, we demonstrate with examples and graphs that our iteration process is faster than all previous procedures, including those of Jungck-SP, Jungck-CR, and Jungck-DK, utilizing MATLAB software. Also, we compare the impact of the initial values and the parameters on the convergence behavior of the proposed iterative process with existing iterative schemes using an example. Finally, we focus on using our iterative technique to approximate the solution of a non-linear integral equation with two delays.
Journal Article
On a discontinuous nonlinear elliptic problem of nonlocal-type with Neumann boundary condition
The objective of this article is to investigate the existence of a weak solution to a class of nonlocal-type problem with Neumann boundary condition, which involves a reaction term that relies on the gradient of the solution, and a multivalued term. Our approach is based on the topological degree theory for a class of weakly upper semi-continuous, locally bounded set-valued operators of (
S
+
) type. The novelty of our work lies in the fact that we are able to manage three major characteristics simultaneously: a convection term, a nonlocal operator and a discontinuous nonlinearity.
Journal Article
The time two-grid algorithm combined with difference scheme for 2D nonlocal nonlinear wave equation
In the paper, we present a time two-grid difference (TGD) method for the approximation of two-dimensional (2D) nonlocal nonlinear wave equation (NNWE). First, the solution is obtained by solving a nonlinear system on the coarse grid (CG), then by using the numerical solutions obtained on the CG we construct a linearized system on the fine grid (FG). Meanwhile the auxiliary values calculated by Lagrange linear interpolation formula. Further, we prove the existence and uniqueness of solution on the CG and FG. Also the stability and convergence is proved strictly through the energy analysis scheme. Finally, two numerical examples are shown, which verify the proposed TGD method is more efficient than the general finite difference (GFD) method.
Journal Article
Existence of multiple unbounded solutions for a three-point boundary value problems on an infinite time scales
In this paper, we consider the second-order three point boundary value problem on time scales with integral boundary conditions on a half-line. We will use the upper and lower solution method along with the Schauder’s fixed point theorem to establish the existence of at least one solution which lies between pairs of unbounded upper and lower solutions. Further, by assuming two pairs of unbounded upper and lower solutions, the Nagumo condition on the nonlinear term involved in the first-order derivative, we will establish the existence of multiple unbounded solutions on an infinite interval by using the topological degree theory. The results of this paper extend the results of
Akcan and Çetin (2018), Akcan and Hamal (2014), Eloe, Kaufmann and Tisdell (2006), and generalize the results of Lian and Geng (2011). Examples are included to illustrate the validation of the results.
Journal Article
Lower and Upper Solutions for System of Differential Equations Involving Homeomorphism and Nonlinear Boundary Conditions
We study the existence of solution to the system of differential equations
(
ϕ
(
u
′
)
)
′
=
f
(
t
,
u
,
u
′
)
with nonlinear boundary conditions
g
(
u
(
0
)
,
u
,
u
′
)
=
0
,
h
(
u
′
(
1
)
,
u
,
u
′
)
=
0
,
where
f
:
[
0
,
1
]
×
R
n
×
R
n
→
R
n
,
g
,
h
:
R
n
×
C
(
[
0
,
1
]
,
R
n
)
×
C
(
[
0
,
1
]
,
R
n
)
→
R
n
are continuous,
ϕ
:
∏
i
=
1
n
(
-
a
i
,
a
i
)
→
R
n
,
0
<
a
i
≤
+
∞
,
ϕ
(
s
)
=
ϕ
1
(
s
1
)
,
⋯
,
ϕ
n
(
s
n
)
and
ϕ
i
:
(
-
a
i
,
a
i
)
→
R
is a one dimensional regular or singular homeomorphism. Our proofs are based on the concept of the lower and upper solutions.
Journal Article
Positive solutions for nonlocal differential equations with concave and convex coefficients
In this paper, we study the positive solutions for nonlocal differential equations with concave and convex coefficients: -A∫01(up(s)+uq(s))dsu′′(t)=f(t,u(t)),t∈(0,1),where 0
Journal Article
A numerical solution of problem for essentially loaded differential equations with an integro-multipoint condition
We study a linear boundary value problem for systems of essentially loaded differential equations with an integro-multipoint condition. We make use of the numerical implementation of the Dzhumabaev parametrization method to obtain the desired result, which is well supported by two numerical examples.
Journal Article
Existence and Uniqueness Results for the Coupled Pantograph System With Caputo Fractional Operator and Hadamard Integral
The main objective of this research involves studying a new novel coupled pantograph system with fractional operators together with nonlocal antiperiodic integral boundary conditions. The system consists of nonlinear pantograph fractional equations which integrate with Caputo fractional operators and Hadamard integrals. A fixed‐point approach has served to study both existence and uniqueness aspects of solutions for the proposed model. The paper investigates Hyers–Ulam stability properties of the developed solution. An appropriate example was provided to confirm the theoretical findings.
Journal Article
The KAM theorem with a large perturbation and application to the network of Duffing oscillators
We prove that there is an invariant torus with the given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for application, we prove that a finite network of Duffing oscillators with periodic external forces possesses Lagrange stability for almost all initial data.
Journal Article
Strict Solutions to Abstract Differential Equations with State-Dependent Nonlocal Conditions
In this paper, we focus on the existence of strict solutions to a class of differential equations with state-dependent nonlocal conditions. Using fixed point theorems and general Gronwall inequality, we give some new conclusions. Moreover, an example is given to illustrate our conclusions valuable.
Journal Article