• Honam Mathematical Journal
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• v.40 no.1
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• pp.1-11
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• 2018

We use Krasnoselskii's fixed point theorem to show that the neutral differential equation $$\frac{d}{dt}[x(t)-a(t)x(\tau(t))]+p(t)x(t)+q(t)x(\tau(t))=0,\;t{\geq}t_0$$, has a positive periodic solution. Some examples are also given to illustrate our results. The results obtained here extend the work of Olach [13].

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.989-1004
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• 2023

In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ς-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.537-555
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• 2023

In this paper, we consider two types of fractional boundary value problems, one of them is an implicit type and the other will be an integro-differential type with nonlocal integral multi-point boundary conditions in the frame of generalized Hilfer fractional derivatives. The existence and uniqueness results are acquired by applying Krasnoselskii's and Banach's fixed point theorems. Some various numerical examples are provided to illustrate and validate our results. Moreover, we get some results in the literature as a special case of our current results.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.245-253
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• 2007

In this paper, the existence of bounded positive solution of the second-order nonlinear neutral differential equations are studied. Some new sufficient conditions are given. Furthermore, examples given show that the results here are almost sharp.

• East Asian mathematical journal
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• v.33 no.3
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• pp.323-331
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• 2017

In this paper, we consider the existence of positive solutions for eigenvalue problems of nonlinear fractional differential equations with singular weights. We give various conditions on f and apply Krasnoselskii's Cone Fixed Point Theorem. As a result, we obtain several existence and nonexistence results corresponding to ${\lambda}$ in certain intervals.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.163-175
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• 2020

The stability of a class of Volterra-type difference equations that include a generalized difference operator ∆_a is investigated using Krasnoselskii's fixed point theorem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.335-350
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• 2016

Based on the notion of $q_k$-derivative introduced by the authors in [17], we prove in this paper existence and uniqueness results for nonlinear second-order impulsive $q_k$-difference equations with anti-periodic boundary conditions. Two results are obtained by applying Banach's contraction mapping principle and Krasnoselskii's fixed point theorem. Some examples are presented to illustrate the results.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.667-680
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• 2020

Our paper deals with the following neutral nonlinear Levin-Nohel integro-differential with variable delay $${\frac{d}{dt}x(t)}+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t-r(t)}}^t}a(t,s)x(s)ds+{\frac{d}{dt}}g(t,x(t-{\tau}(t)))=0.$$ By using Krasnoselskii's fixed point theorem we obtain the existence of periodic and positive periodic solutions and by contraction mapping principle we obtain the existence of a unique periodic solution. An example is given to illustrate this work.