• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.209-220
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• 2007

In this paper, the existence and multiplicity of solutions of three-point p-Laplacian boundary value problems at resonance with one-sided Nagumo condition are studied by using degree theory and upper and lower solutions method. Some known results are improved.

• Proceedings of the Korean Vacuum Society Conference
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• 2010.02a
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• pp.472-472
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• 2010

The tomography has played a key role in tokamak plasma diagnostics for image reconstruction. The Phillips-Tikhonov (P-T) regularization method was attempted in this work to reconstruct cross-sectional phantom images of the plasma by minimizing the gradient between adjacent pixel data. Recent studies about the comparison of the several tomographic reconstruction methods showed that the P-T method produced more accurate results. We have studied existing Laplacian matrix used in Phillips-Tikhonov regularization method and developed modified Laplacian matrix (Modified L). The comparison of the reconstruction result by the modified L and existing L showed that modified L produced more accurate result. The difference was significantly pronounced when a portion of plasma was reconstructed. These results can be utilized in the Edge Plasma diagnostics; especially in divertor diagnostics on tokamak a large impact is expected. In addition, accurate reconstruction results from received data in only one direction were confirmed through phantom test by using P-T method with modified L. These results can be applied to the tangentially viewing pin-hole camera diagnostics on tokamak.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1179-1192
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• 2012

In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ in ${\Omega}{\times}[0,T]$, with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on ${\beta}$, $f$ and $p$.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1017-1030
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• 2012

We consider forced second order differential equation with $p$-Laplacian and nonlinearities given by a Riemann-Stieltjes integrals in the form of $$(p(t){\phi}_{\gamma}(x^{\prime}(t)))^{\prime}+q_0(t){\phi}_{\gamma}(x(t))+{\int}^b_0q(t,s){\phi}_{{\alpha}(s)}(x(t))d{\zeta}(s)=e(t)$$, where ${\phi}_{\alpha}(u):={\mid}u{\mid}^{\alpha}\;sgn\;u$, ${\gamma}$, $b{\in}(0,{\infty})$, ${\alpha}{\in}C[0,b)$ is strictly increasing such that $0{\leq}{\alpha}(0)<{\gamma}<{\alpha}(b-)$, $p$, $q_0$, $e{\in}C([t_0,{\infty}),{\mathbb{R}})$ with $p(t)>0$ on $[t_0,{\infty})$, $q{\in}C([0,{\infty}){\times}[0,b))$, and ${\zeta}:[0,b){\rightarrow}{\mathbb{R}}$ is nondecreasing. Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. As special cases, our work generalizes, unifies, and improves many existing results in the literature.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1211-1220
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• 2009

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.451-459
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• 2021

We propose the infinity wave equation which can be derived from the exponential wave equation through the limit p → ∞. The solution of infinity Laplacian equation can be considered as a static solution of the infinity wave equation. We present basic observations and find some special solutions.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.725-737
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• 2024

This article introduces the concepts of Energy and Laplacian Energy (LE) of Domination in Hesitancy fuzzy graph (DHFG). Also, the adjacency matrix of a DHFG is defined and proposed the definition of the energy of domination in hesitancy fuzzy graph, and Laplacian energy of domination in hesitancy fuzzy graph is given.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.6C
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• pp.384-390
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• 2011

The paper derives formulas for the mean-squared error distortion and resulting signal-to-noise (SNR) ratio of a fixed-rate scalar quantizer designed optimally in the minimum mean-squared error sense for a Gaussian density with the standard deviation ${\sigma}_q$ when it is mismatched to a Laplacian density with the standard deviation ${\sigma}_q$. The SNR formulas, based on the key parameter and Bennett's integral, are found accurate for a wide range of $p\({\equiv}\frac{\sigma_p}{\sigma_q}\){\geqq}0.25$. Also an upper bound to the SNR is derived, which becomes tighter with increasing rate R and indicates that the SNR behaves asymptotically as $\frac{20\sqrt{3{\ln}2}}{{\rho}{\ln}10}\;{\sqrt{R}}$ dB.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.137-152
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• 2014

In this paper, we prove, in the spirit of [3, 12, 20, 22, 23], the existence of infinitely many small solutions to the following quasilinear elliptic equation $-{\Delta}_{p(x)}u+{\mid}u{\mid}^{p(x)-2}u={\mid}u{\mid}^{q(x)-2}u+{\lambda}f(x,u)$ in a smooth bounded domain ${\Omega}$ of ${\mathbb{R}}^N$. We also assume that $\{q(x)=p^*(x)\}{\neq}{\emptyset}$, where $p^*(x)$ = Np(x)/(N - p(x)) is the critical Sobolev exponent for variable exponents. The proof is based on a new version of the symmetric mountainpass lemma due to Kajikiya [22], and property of these solutions are also obtained.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.117-121
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• 2009

For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.