• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.877-882
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• 2010

In this paper, a third-order three-point boundary value problem on time scales is considered. We establish criteria for the existence of a solution and a positive solution by using the Leray-Schauder fixed point theorem. An example is also given to illustrate our results.

• 호남수학학술지
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• 제19권1호
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• pp.71-80
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• 1997

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.121-130
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• 2017

This study is concerned with the existence of positive solution for the following nonlinear elliptic system $$\{-M_1(\int_{\Omega}{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^pdx)div({\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)\\{\hfill{120}}={\mid}x{\mid}^{-(a+1)p+c_1}\({\alpha}_1A_1(x)f(v)+{\beta}_1B_1(x)h(u)\),\;x{\in}{\Omega},\\-M_2(\int_{\Omega}{\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^qdx)div({\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^{q-2}{\nabla}v)\\{\hfill{120}}={\mid}x{\mid}^{-(b+1)q+c_2}\({\alpha}_2A_2(x)g(u)+{\beta}_2B_2(x)k(v)\),\;x{\in}{\Omega},\\{u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}$ is a bounded smooth domain of ${\mathbb{R}}^N$ with $0{\in}{\Omega}$, 1 < p, q < N, $0{\leq}a$ < $\frac{N-p}{p}$, $0{\leq}b$ < $\frac{N-q}{q}$ and ${\alpha}_i,{\beta}_i,c_i$ are positive parameters. Here $M_i,A_i,B_i,f,g,h,k$ are continuous functions and we discuss the existence of positive solution when they satisfy certain additional conditions. Our approach is based on the sub and super solutions method.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.363-374
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• 2007

In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.329-337
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• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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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.

• 충청수학회지
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• 제20권3호
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• pp.231-243
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• 2007

In this paper, we study a Lotka-Volterra type simple food chain model. We investigate the positive coexistence of the steady states to the model and give some results for the extinction of species under certain assumptions which can be interpreted as Domino effect and Biological control. The methods of a decoupling operator and the fixed point index theory on a positive cone are used as well as the comparison argument. Numerical evidences for our results also are provided.

• 대한수학회논문집
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• 제23권1호
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• pp.61-65
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• 2008

In this paper we prove that every positive solution of the third order rational difference equation $$x_{n+1}\;=\;\frac{{\beta}x_n\;+\;x_{n-2}}{A\;+\;Bx_n\;+\;x_{n-2}}$ converges to the positive equilibrium point $$\bar{x}\;=\;\frac{{\beta}\;+\;1\;-\;A}{B\;+\;1}$, where $0\;<\;{\beta}\;{\leq}\;B$, $1\;<\;A\;<\;{\beta}\;+\;1$

• East Asian mathematical journal
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• 제40권1호
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• pp.51-61
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• 2024

In this work, we study the existence of a positive solution for nonlinear fractional differential equation with a singular weight. For the proof, we introduce newly defined solution operator and use well-known Krasnoselski's fixed point theorem. We also give an example with a singular weight which may not be integrable.

• East Asian mathematical journal
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• 제34권5호
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• pp.703-713
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• 2018

Let $N{\geq}3$, $2^*=2N/(N-2)$ and $p{\in}(2,2^*)$. Our purpose in this paper is to consider multiple existence of solutions of problem $$-{\Delta}u-{\frac{\mu}{{\mid}x{\mid}^2}}+{\alpha}u={\mid}u{\mid}^{p-2}u+{\lambda}f\;u{\in}H^1({\mathbb{R}}^n)$$, where a, ${\lambda}$ > 0, ${\mu}{\in}(0,(N-2)^2/4)f{\in}H^{-1}({\mathbb{R}}^N)$, $f{\geq}0$ and $f{\neq}0$.