• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.65-71
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• 2019

This paper is concerned with the existence of positive solutions of the nonlinear Neumann boundary value problems $$\{u^{{\prime}{\prime}}+a(t)u={\lambda}b(t)f(u),\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$, where $a,b{\in}C[0,1]$ with $a(t)>0,\;b(t){\geq}0$ and the Green's function of the linear problem $$\{u^{{\prime}{\prime}}+a(t)u=0,\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$ may change its sign on $[0,1]{\times}[0,1]$. Our analysis relies on the Leray-Schauder fixed point theorem.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.305-320
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• 2024

We consider a mathematical model which describes the quasistatic contact of electro-viscoelastic rod with an obstacle. We use a modified Kelvin-Voigt viscoelastic constitutive law in which the elasticity operator is nonlinear and locally Lipschitz continuous, taking into account the piezoelectric effect of the material. We model the contact with a general damped response condition. We establish a local existence and uniqueness result of the solution by using arguments of time-dependent nonlinear equations and Schauder's fixed-point theorem and obtain a global existence for small enough data.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.635-646
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• 2012

This paper is concerned with an SIRS epidemic model with spatial diffusion and time delay representing the length of the immunity period. By using a new cross iteration scheme and Schauder's fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a newfashioned pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the uninfected steady state and the infected steady state.

• East Asian mathematical journal
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• v.15 no.1
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• pp.91-103
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• 1999

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.641-651
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• 2014

Because of difficulty of using Schauder's fixed point theorem to the polynomial-like iterative equation, a lots of work are contributed to the existence of solutions for the polynomial-like iterative equation on compact set. In this paper, by applying the Schauder-Tychonoff fixed point theorem we discuss monotone solutions and convex solutions of the polynomial-like iterative equation on an open set (possibly unbounded) in $\mathbb{R}^N$. More concretely, by considering a partial order in $\mathbb{R}^N$ defined by an order cone, we prove the existence of increasing and decreasing solutions of the polynomial-like iterative equation on an open set and further obtain the conditions under which the solutions are convex in the order.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.877-894
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• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.237-249
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• 2023

In this paper, by means of the Schauder fixed point theorem and Arzela-Ascoli theorem, the existence and uniqueness of solutions for a class of not instantaneous impulsive problems of nonlinear fractional functional Volterra-Fredholm integro-differential equations are investigated. An example is given to illustrate the main results.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.497-502
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• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.305-316
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• 2022

We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.