• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• 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.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.243-256
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• 2010

This paper is concerned with the neutral impulsive functional differential equations $$\{{x'(t)\;+\;a(t)x(t)\;=\;f(t,\;x(t\;-\;\tau(t),\;x'(t\;-\;\delta(t))),\;a.e.\;t\;{\in}\;R, \atop {\Delta}x(t_k)\;=\;b_kx(t_k),\;k\;{\in}\;Z.$$ Sufficient conditions for the existence of at least three positive T-periodic solution are established. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.445-459
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• 2006

In this paper cellular neural networks with continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality technique. The results of this paper are new and they complement previously known results.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.29-40
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• 2009

Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.13-16
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• 1998

For continuous maps f of the circle to itself, we show that (1) every $\omega$-limit point is recurrent (or almost periodic) if and only if every $\omega$-limit set is minimal, (2) every $\omega$-limit set is almost periodic, then every $\omega$-limit set contains only one minimal set.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.297-314
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• 2021

This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir-Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.353-361
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• 2007

In this paper, we prove the existence of multiple solutions for Neumann and periodic problems. Our main tools are recent general multiplicity theorems proposed by B. Ricceri.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.863-868
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• 2011

The purpose of this paper is to study the orbit behaviours near almost periodic points. We introduce notions of uniformly recurrent and u-recurrent points and investigate some relationships between these properties.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.303-322
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• 2021

The concepts of new classes of mappings are introduced in the spaces which are more general space than the usual metric spaces. The existence and uniqueness of common fixed points and fixed point results are established in the setting of complete complex valued b-metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in the framework of a complete complex valued b-metric spaces.