• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.163-174
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• 1991

This is a continuation of the author's previous work [17]. In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian [10] and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality [5] and its subsequent generalizations due to Brezis et al [4], Takahashk [23], Shih and Tan [19], Simons [20], and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan [19].

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.127-139
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• 2007

In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.245-252
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• 2015

This paper is in continuation of the paper very recently published [New Laplace transforms of Kummer's confluent hypergeometric functions, Math. Comp. Modelling, 55 (2012), 1068-1071]. In this paper, our main objective is to show one can obtain so far unknown Laplace transforms of three rather general cases of generalized hypergeometric function $_2F_2(x)$ by employing generalized Watson's, Dixon's and Whipple's summation theorems for the series $_3F_2$ obtained earlier in a series of three research papers by Lavoie et al. [5, 6, 7]. The results established in this paper may be useful in theoretical physics, engineering and mathematics.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.409-421
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• 2014

This paper deals with the superlinear elliptic problem without Ambrosetti and Rabinowitz type growth condition of the form: $$\{-div\((1+\frac{|{\nabla}u|^{p(x)}}{\sqrt{1+|{\nabla}u|^{2p(x)}}}})|{\nabla}u|^{p(x)-2}{\nabla}u\)={\lambda}f(x,u)\;a.e.\;in\;{\Omega}\\u=0,\;on\;{\partial}{\Omega}$$ where ${\Omega}{\subset}R^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\lambda}$ > 0 is a parameter. The purpose of this paper is to obtain the existence results of nontrivial solutions for every parameter ${\lambda}$. Firstly, by using the mountain pass theorem a nontrivial solution is constructed for almost every parameter ${\lambda}$ > 0. Then we consider the continuation of the solutions. Our results are a generalization of that of Manuela Rodrigues.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.361-372
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• 2006

In this paper, we consider the multi-point boundary value problems for one-dimensional p-Laplacian at resonance: $({\phi}_p(x'(t)))'=f(t,x(t),x'(t))$, subject to the boundary value conditions: ${\phi}_p(x'(0))={\sum}^{n-2}_{i=1}{\alpha}_i{\phi}_p(x'({\epsilon}i)),\;{\phi}_p(x'(1))={\sum}^{m-2}_{i=1}{\beta}_j{\phi}_p(x'({\eta}_j))$ where ${\phi}_p(s)=/s/^{p-2}s,p>1,\;{\alpha}_i(1,{\le}i{\le}n-2){\in}R,{\beta}_j(1{\le}j{\le}m-2){\in}R,0<{\epsilon}_1<{\epsilon}_2<...<{\epsilon}_{n-2}1,\;0<{\eta}1<{\eta}2<...<{\eta}_{m-2}<1$, By applying the extension of Mawhin's continuation theorem, we prove the existence of at least one solution. Our result is new.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.161-171
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• 2012

We consider the fourth-order differential equation with one-dimensional $p$-Laplacian (${\phi}_p(x^{\prime\prime}(t)))^{\prime\prime}=f(t,x(t),x^{\prime}(t),x^{\prime\prime}(t)$) a.e. $t{\in}[0,1]$, subject to the boundary conditions $x^{\prime\prime}}(0)=0$, $({\phi}_p(x^{\prime\prime}(t)))^{\prime}{\mid}_{t=0}=0$, $x(0)={\sum}_{i=1}^n{\mu}_ix({\xi}_i)$, $x(t)=x(1-t)$, $t{\in}[0,1]$, where ${\phi}_p(s)={\mid}s{\mid}^{p-2}s$, $p$ > 1, 0 < ${\xi}_1$ < ${\xi}_2$ < ${\cdots}$ < ${\xi}_n$ < $\frac{1}{2}$, ${\mu}_i{\in}\mathbb{R}$, $i=1$, 2, ${\cdots}$, $n$, ${\sum}_{i=1}^n{\mu}_i=1$ and $f:[0,1]{\times}\mathbb{R}^3{\rightarrow}\mathbb{R}$ is a $L^1$-Carath$\acute{e}$odory function with $f(t,u,v,w)=f(1-t,u,-v,w)$ for $(t,u,v,w){\in}[0,1]{\times}\mathbb{R}^3$. We obtain the existence of at least one nonconstant symmetric solution by applying an extension of Mawhin's continuation theorem due to Ge. Furthermore, an example is given to illustrate the results.