• Korean Journal of Mathematics
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• v.16 no.2
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• pp.243-257
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• 2008

We seek the sign changing periodic solutions of the nonlinear wave equation $u_{tt}-u_{xx}=a(x,t)g(u)$ under Dirichlet boundary and periodic conditions. We show that the problem has at least one solution or two solutions whether $\frac{1}{2}g(u)u-G(u)$ is bounded or not.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1269-1284
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• 2022

This paper is concerned with the following Schrödinger-Poisson system $$\{\begin{array}{lll}-{\Delta}u+V(x)u+K(x){\phi}u=a(x){\mid}u{\mid}^{p-2}u&&\text{ in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=K(x)u^2&&\text{ in }{\mathbb{R}}^3,\end{array}$$ where 4 < p < 6. For the case that K is nonnegative, V and a are indefinite, we prove the above problem possesses one ground state sign-changing solution with exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions is larger than that of the ground state solutions. The novelty of this paper is that the potential a is indefinite and allowed to vanish at infinity. In this sense, we complement the existing results obtained by Batista and Furtado [5].

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1181-1209
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• 2021

In the present paper, we are concerned with the existence of ground state sign-changing solutions for the following Schrödinger-Poisson-Kirchhoff system $$\;\{\begin{array}{lll}-(1+b{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+k(x){\phi}u={\lambda}f(x)u+{\mid}u{\mid}^4u,&&\text{in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=k(x)u^2,&&\text{in }{\mathbb{R}}^3,\end{array}$$ where b > 0, V (x), k(x) and f(x) are positive continuous smooth functions; 0 < λ < λ₁ and λ₁ is the first eigenvalue of the problem -∆u + V(x)u = λf(x)u in H. With the help of the constraint variational method, we obtain that the Schrödinger-Poisson-Kirchhoff type system possesses at least one ground state sign-changing solution for all b > 0 and 0 < λ < λ₁. Moreover, we prove that its energy is strictly larger than twice that of the ground state solutions of Nehari type.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.411-422
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• 2010

By using the fixed point index theory, we investigate the existence of at least two positive solutions for p-Laplace equation with sign-changing nonlinear terms $(\varphi_p(u'))'+a(t)f(t,u(t),u'(t))=0$, subject to some boundary conditions. As an application, we also give an example to illustrate our results.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.75-82
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• 2014

In this paper, we consider the periodic boundary value problem with sign changing nonlinearity $$u^{{\prime}{\prime}{\prime}}+{\rho}^3u=f(t,u),\;t{\in}[0,2{\pi}]$$, subject to the boundary value conditions: $$u^{(i)}(0)=u^{(i)}(2{\pi}),\;i=0,1,2$$, where ${\rho}{\in}(o,{\frac{1}{\sqrt{3}}})$ is a positive constant and f(t, u) is a continuous function. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is the nonlinear term f may change sign.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.37-51
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• 2004

In this paper, we consider the asymptotic behavior of solutions of the forced nonlinear neutral difference equation $\Delta[x(n)-\sumpi(n)x(n-k_i)]+\sumqj(n)f(x(n-\iota_j))=r(n)$ with sign changing coefficients. Some sufficient conditions for every solution of (*) to tend to zero are established. The results extend and improve some known theorems in literature.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.445-468
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• 2020

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

• Journal of KIISE:Computing Practices and Letters
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• v.8 no.2
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• pp.231-239
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• 2002

This paper gives a comprehensive overview of the SSO solution design on the intranet. SSO described in this paper is based on LDAP, PKI and CA. We designed the data structure to hold many various application services by changing the attribute and DN of LDAP DB. We built LDAP DB using the employee records stored in our organization database. LDAP DB is routinely updated from the database. CA Server that depends on PKI is used to issue the certificates. SHTTP based on SSL is used to protect the data between certificate server and the intranet users.

• Journal of Korean Public Health Nursing
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• v.12 no.2
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• pp.185-200
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• 1998

It has been contributed to public health that the hospital has multiplied in the aspect of number and has been a large size with development of modern medical science, meanwhile the problem of hospital infection is coming out seriously. Respiratory hospital infection among hospital infections develops, very commonly from patients having taken the operation of intubation or tracheostomy, which results from a big factor that the infection developed from medical appliances used for respiration aids, contamination of solution and infection of medical staff. This study is separated into four steps-the time to use normal saline and distillation water for storaging catheter which are the cause of the infection of solution to store distillation water and catheter, not to say the catheter used when the patient who should get tracheostomy operation takes suction. The purpose of this study is to offer the basic data which are needed to check contamination degree as time goes by and nurse intervention and grope for a new nursing intervention. The target of this study is hospitalized 1D an intensive care unit having 700 sickbeds which is located in IKSAN city and it targeted patients before 7 days passed after an operaion of a tracheostormy. Materials collected were analyzed by SPSS PC+ figures program. The result of this study were as follows ; 1. The gradual contamination levels of the normal saline used In suction are showing that colony increase in proportion to the length of time. 2. while colony increases in normal saline with the lapse of time. distillation water mixed with 5cc of potadine did not show any sign of the formation of colony from its preparation until it was used for 8 hours. 3. Such variables as the period of intubation insertion. the length of hospitalization in I.C.U. the age and the level of contamination of normal saline have no inter-relationship. Therefore. as the length of normal saline used In suction. the contamination level increases with the excelleration of the contamination speed. 4. Regarding the number of suction and the contamination level of the normal saline. We can observe correlation contamination level in the 3 step of suction(mean value:13.4) and the saline which was used for one hours(r=0.702. P=0.00l). four hours(r=0.694. P=0.00l). eight hours(r=0.488. P=0.029). Further we can observe contamination in the 4 step of suction (mean value: 17 .8) well as saline used for eight hours; [for one hours (r=0.64l. P=0.002). four hours (r=0.670. P=0.00l). eight hours (r=0.57 4. P=0.008)]. Thesedays clinics use normal saline by changing it. three times a day. however. the timing of saline change and the current suction methoed should be changed given the one hour used normal saline contamination number 79.850. Regarding the number of suction and the contamination lend of the normal saline.