• Nonlinear Functional Analysis and Applications
• /
• 제27권3호
• /
• pp.649-662
• /
• 2022

This paper is concerned with the existence of solutions for a class of 𝚽-Kirchhoff type equations with critical exponent in Orlicz-Sobolev spaces. Our technical approach is based on variational methods.

• East Asian mathematical journal
• /
• 제33권5호
• /
• pp.511-525
• /
• 2017

We introduce an extrapolated higher order characteristic finite element method to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergence in both the temporal direction and the spatial direction in $L^2$ normed space is established and some computational results to support our theoretical results are presented.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1409-1419
• /
• 2017

We introduce an extrapolated Crank-Nicolson characteristic finite element method to approximate solutions of a convection dominated Sobolev equation. We obtain the higher order of convergence in both the spatial direction and the temporal direction in $L^2$ normed space for the extrapolated Crank-Nicolson characteristic finite element method.

• East Asian mathematical journal
• /
• 제33권3호
• /
• pp.295-308
• /
• 2017

We introduce a Crank-Nicolson characteristic finite element method to construct approximate solutions of a nonlinear Sobolev equation with a convection term. And for the Crank-Nicolson characteristic finite element method, we obtain the higher order of convergence in the temporal direction and in the spatial direction in $L^2$ normed space.

• East Asian mathematical journal
• /
• 제32권5호
• /
• pp.729-744
• /
• 2016

A Crank-Nicolson characteristic finite element method is introduced to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergences in the temporal direction and in the spatial direction in $L^2$ normed space are verified for the Crank-Nicolson characteristic finite element method.

• 대한수학회보
• /
• 제33권1호
• /
• pp.135-170
• /
• 1996

Recently many people have studied the Sobolev orthogonal polynomials, that is, polynomials which are orthogonal relative to a symmetric bilinear form $\phi(\cdot,\cdot)$ defined by $$ (1.1) $\phi(p,q) := (p,q)_N = \sum_{k=0}^{N} \int_{R}p^(k) (x)q^(k) (x) d\mu_k, $$ where each $d\mu_k$ is a signed Borel measure on the real line $R$ with finite moments of all orders. For the brief history on this subject, we refer to the survey article Ronveaux [13] and Marcellan and et al [10].

• 대한수학회지
• /
• 제32권4호
• /
• pp.815-834
• /
• 1995

Let $\Omega$ be a rectangular domain in $R^2$ with boundary $\partial\Omega$, and T be a positive real number such that $0 < T < \infty$.

• 대한수학회논문집
• /
• 제14권1호
• /
• pp.223-231
• /
• 1999

In this paper we prove the existence of solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal conditions. The results are obtained by using compact semigroups and the Schauder fixed point theorem.

• East Asian mathematical journal
• /
• 제37권5호
• /
• pp.591-598
• /
• 2021

In this paper we study the Cauchy problem for the Chern-Simons gauged O(3) sigma model. We prove the local existence of solutions with low regularity initial data, observing null forms of the system and applying bilinear estimates for wave-Sobolev space H^{s, b}.

• 대한수학회지
• /
• 제47권3호
• /
• pp.547-572
• /
• 2010

We study existence of positive solutions of the classical nonlinear Schr$\ddot{o}$dinger equation $-{\Delta}u\;+\;V(x)u\;-\;f(x,\;u)\;-\;H(x)u^{2*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$. In fact, we consider the following more general quasi-linear Schr$\ddot{o}$odinger equation $-div(|{\nabla}u|^{m-2}{\nabla}u)\;+\;V(x)u^{m-1}$ $-f(x,\;u)\;-\;H(x)u^{m^*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$, where m $\in$ (1, n) is a positive number and $m^*\;:=\;\frac{mn}{n-m}\;>\;0$, is the corresponding critical Sobolev embedding number in $\mathbb{R}^n$. Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.