• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.1051-1065
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• 2012

In this paper, the global stability and almost periodicity are investigated for generalized Hopfield neural networks with time-varying neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results. Finally, an example is given to demonstrate the effectiveness of our results.

• 대한수학회보
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• 제48권1호
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• pp.213-221
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• 2011

In this paper, we establish a multiple critical points theorem for a one-parameter family of non-smooth functionals. The obtained result is then exploited to prove a multiplicity result for a class of periodic eigenvalue problems driven by the p-Laplacian and with a non-smooth potential. Under suitable assumptions, we locate an open subinterval of the eigenvalue.

• 대한수학회보
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• 제49권3호
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• pp.455-463
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• 2012

In this paper, by using degree theory, we consider a kind of higher-order Li$\acute{e}$enard type $p$-Laplacian differential equation as follows $$({\phi}_p(x^{(m)}))^{(m)}+f(x)x^{\prime}+g(t,x)=e(t)$$. Some new results on the existence of anti-periodic solutions for above equation are obtained.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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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.

• 대한수학회지
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• 제44권4호
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• pp.873-887
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• 2007

In this paper cellular neutral networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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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.

• 대한수학회지
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• 제37권5호
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• pp.707-720
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• 2000

Conley index is used study bifurcation from equilibria of full bounded solutions to parameter dependent families of ordinary differential equations of the form {{{{ {dx} over {dt} }}}} =$\varepsilon$F(x, t, $\mu$). It is assumed that F(x, t,$\mu$) is uniformly almost periodic in t.

• 대한수학회지
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• 제42권2호
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• pp.191-202
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• 2005

A condition on forcing term insuring the multiplicity of Dirichlet-periodic solutions of nonlinear dissipative hyperbolic equations is discussed. The nonlinear term is assumed to have coercive growth.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.143-152
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• 2010

Based on the Exp-function method and a suitable transformation, new generalized solitonary solutions including free parameters of the MDI and Sawada-Kotera equations with variable coefficients are obtained, form which solitary wave solutions and periodic solutions including some known solutions reported in open literature are derived as special cases. The free parameters in the obtained generalized solitonary solutions might imply some meaningful results in the physical models. It is shown that the Exp-function method provides a very effective and important new method for nonlinear evolution equations with variable coefficients.

• 충청수학회지
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• 제22권2호
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• pp.251-259
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• 2009

We investigate the multiple solutions for the nonlinear parabolic boundary value problem with jumping nonlinearity crossing two eigenvalues. We show the existence of at least four nontrivial periodic solutions for the parabolic boundary value problem. We restrict ourselves to the real Hilbert space and obtain this result by the geometry of the mapping.