• Communications of the Korean Mathematical Society
• /
• v.11 no.4
• /
• pp.1003-1013
• /
• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

• 한국전산유체공학회:학술대회논문집
• /
• 2003.10a
• /
• pp.126-127
• /
• 2003

In the generalized characteristic coordinate system (GCCS) proposed by Wu and Shi [1], the frame moves at a speed which is a linear combination of the convective speed and the sound speed, thus unifying the classical Eulerian approach, Lagrangian approach, and the unified coordinate system (UCS) of Hui and his co-workers [2]. Here some properties of Euler equations in the GCCS are studied and the advantages of GCCS in capturing expansion fans and shock waves are demonstrated by the results of numerical tests.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.337-346
• /
• 2000

The geodesic equation in a two-dimensional Finsler space is given by the differential equation of the Weierstrass form. In the present paper, we express the differential equations of geodesics in a two-dimensional Finsler space with a generalized Kropina metric.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.221-238
• /
• 2011

We prove the Hyers-Ulam stability of generalized Jensen's equations in Banach modules over a unital $C^{\ast}$-algebra. It is applied to show the stability of generalized Jensen's equations in a Hilbert module over a unital $C^{\ast}$-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital $C^{\ast}$-algebra.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.793-809
• /
• 2021

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order α (1 < α < 2). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.

• Journal of the Chungcheong Mathematical Society
• /
• v.16 no.1
• /
• pp.97-101
• /
• 2003

We investigate generalized Baxter equations on Banach algebras. This is applied to understand generalized anti-derivations on Banach *-algebras.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.1041-1054
• /
• 2014

Let $P{\geq}3$ be an integer and let ($U_n$) and ($V_n$) denote generalized Fibonacci and Lucas sequences defined by $U_0=0$, $U_1=1$; $V_0= 2$, $V_1=P$, and $U_{n+1}=PU_n-U_{n-1}$, $V_{n+1}=PV_n-V_{n-1}$ for $n{\geq}1$. In this study, when P is odd, we solve the equations $V_n=kx^2$ and $V_n=2kx^2$ with k | P and k > 1. Then, when k | P and k > 1, we solve some other equations such as $U_n=kx^2$, $U_n=2kx^2$, $U_n=3kx^2$, $V_n=kx^2{\mp}1$, $V_n=2kx^2{\mp}1$, and $U_n=kx^2{\mp}1$. Moreover, when P is odd, we solve the equations $V_n=wx^2+1$ and $V_n=wx^2-1$ for w = 2, 3, 6. After that, we solve some Diophantine equations.

• 한국전산유체공학회:학술대회논문집
• /
• 2000.10a
• /
• pp.60-65
• /
• 2000

This paper presents the analysis of flowfield inside a low-density nozzle and its plume into near vacuum. The generalized hydrodynamics equations are numerically solved for the purpose with the help of modern computational fluid dynamic methods. The results taken along the nozzle are compared with those of Navier-Stokes equations and available experimental data. The plume outside the nozzle is also analyzed in order to examine the adverse effects of its impingements.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1845-1858
• /
• 2018

This paper is to consider the generalized Fermat difference equations with different types which ever considered by Li [14], Ishizaki and Korhonen [9], Zhang [26] and Liu [15-18], respectively. Some new observations and results on these equations will be given.

• Journal of applied mathematics & informatics
• /
• v.34 no.3_4
• /
• pp.193-206
• /
• 2016

In this paper, we study boundary value problems for fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.