A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their c...A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds.展开更多
This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple pos...This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.展开更多
The existence of common fixed points and invariant approximations for pointwise R- subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class...The existence of common fixed points and invariant approximations for pointwise R- subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class of noncommuting mappings.展开更多
A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative,...A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.展开更多
By employing the generalized Riccati transformation technique,we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral del...By employing the generalized Riccati transformation technique,we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation [r(t)[y(t)+p(t)y(■(t))]~Δ]~Δ+q(t)f(y((δ(t)))=0 on a time scale■.The results improve some oscillation results for neutral delay dynamic equations and in the special case when■our results cover and improve the oscillation results for second- order neutral delay differential equations established by Li and Liu[Canad.J.Math.,48(1996), 871 886].When■,our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh[Comp.Math.Appl.,36(1998),123-132].When ■ ■our results are essentially new.Some examples illustrating our main results are given.展开更多
Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either e...Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved.展开更多
We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for ...We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.展开更多
文摘A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds.
基金Supported by the National Natural Science Foundation of China(No.10571111)the fund of Shandong Education Committee(J07WH08).
文摘This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.
文摘The existence of common fixed points and invariant approximations for pointwise R- subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class of noncommuting mappings.
基金Supported by Grant No.201/01/1451 of the Grant Agency of Czech Republicthe Council of Czech Government J14/98:153100011
文摘A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.
文摘By employing the generalized Riccati transformation technique,we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation [r(t)[y(t)+p(t)y(■(t))]~Δ]~Δ+q(t)f(y((δ(t)))=0 on a time scale■.The results improve some oscillation results for neutral delay dynamic equations and in the special case when■our results cover and improve the oscillation results for second- order neutral delay differential equations established by Li and Liu[Canad.J.Math.,48(1996), 871 886].When■,our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh[Comp.Math.Appl.,36(1998),123-132].When ■ ■our results are essentially new.Some examples illustrating our main results are given.
文摘Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved.
基金The first and third authors have been supported in part by Ministerio de Cienciay Tecnología(Spain)MTM2004-06652-C03-03
文摘We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.
