• Honam Mathematical Journal
• /
• v.35 no.4
• /
• pp.679-681
• /
• 2013

In this paper, we raise a question regarding existence and uniqueness of the steady-state solution of a type of Kolmogorov forward equation. We prove that the question has a positive answer for trivial vector fields, and also provide examples which show that the compactness assumption is necessary.

• Journal of applied mathematics & informatics
• /
• v.26 no.5_6
• /
• pp.1037-1048
• /
• 2008

The purpose of this paper is to present a differential equation with delay from biological excitable medium. Existence, uniqueness and data dependence (monotony, continuity, differentiability with respect to parameter) results for the solution of the Cauchy problem of biological excitable medium are obtained using weakly Picard operator theory.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.2
• /
• pp.337-346
• /
• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.

• The Pure and Applied Mathematics
• /
• v.10 no.1
• /
• pp.13-23
• /
• 2003

The purpose of this paper is to prove the fundamental existence and uniqueness theorems for lightlike curves in a 6-dimensional semi-Euclidean space Rq of index q, since the general n-dimensional cases are too complicated.

• Honam Mathematical Journal
• /
• v.37 no.1
• /
• pp.99-112
• /
• 2015

In this paper we consider the periodic Cauchy problem for the generalized two-component Hunter-Saxton system with analytic initial data and we prove a Cauchy-Kowalevski type theorem for the generalized two-component Hunter-Saxton system, that establishes the existence and uniqueness of real analytic solutions.

• Korean Journal of Mathematics
• /
• v.27 no.3
• /
• pp.819-830
• /
• 2019

This paper is mainly concerned with the existence and uniqueness of fixed points of $f:X^k{\rightarrow}X$, $k{\in}{\mathbb{N}}$, where X is a quasi-partial metric space and mapping f satisfies appropriate conditions. Results are also supported with relevant examples.

• East Asian mathematical journal
• /
• v.40 no.1
• /
• pp.37-50
• /
• 2024

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

• Communications of the Korean Mathematical Society
• /
• v.12 no.4
• /
• pp.1039-1064
• /
• 1997

Existence and Uniqueness for Volterra equations (VE) with a weak regularity assumption on A, the relative closedness of A are investigaed by means of the Laplace transform theory. Also, (VE) are studied by means of the method of convoluted solution operator families.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.3
• /
• pp.321-325
• /
• 2007

We prove the Medina's results about the existence and uniqueness of solutions of discrete Volterra equations of convolution type in weighted spaces, by using the well-known Contraction Mapping Principle.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1997.10a
• /
• pp.226-229
• /
• 1997