Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions hav...Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.展开更多
A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhi...A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.展开更多
We consider a Hilbert boundary value problem with an unknown parametric function on arbitrary infinite straight line passing through the origin. We propose to transform the Hilbert boundary value problem to Riemann bo...We consider a Hilbert boundary value problem with an unknown parametric function on arbitrary infinite straight line passing through the origin. We propose to transform the Hilbert boundary value problem to Riemann boundary value problem, and address it by defining symmetric extension for holomorphic functions about an arbitrary straight line passing through the origin. Finally, we develop the general solution and the solvable conditions for the Hilbert boundary value problem.展开更多
This paper investigates existence of positive solutions of singular sub-linear boundary value problems on a half-line. Necessary and sufficient conditions for the existence of positive continuous solutions or smooth s...This paper investigates existence of positive solutions of singular sub-linear boundary value problems on a half-line. Necessary and sufficient conditions for the existence of positive continuous solutions or smooth solutions on [0, ∞] are given by constructing new lower and upper solutions.展开更多
In this paper, we are concerned with the existence of a second-order differential equation with m-point boundary conditions on the half line. The existence results are proved by the Leray-Scha¨uder point theorem ...In this paper, we are concerned with the existence of a second-order differential equation with m-point boundary conditions on the half line. The existence results are proved by the Leray-Scha¨uder point theorem in a special Banach space. Green function plays an important role in the proof and its discussion is very interesting. The results obtained generalize those in the previous references.展开更多
We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems： additional edge singularities are known to develop in that case. This pa...We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems： additional edge singularities are known to develop in that case. This paper includes a rigorous error analysis proving the convergence of our numerical scheme. Three types of examples are covered： the Laplace equation in free space, the linear elasticity equation in free space, and in half space.展开更多
The Method Of Lines (MOL) and Scheifele’s G-functions in the design of algorithms adapted for the numeric integration of parabolic Partial Differential Equations (PDE) in one space dimension are applied. The semi-dis...The Method Of Lines (MOL) and Scheifele’s G-functions in the design of algorithms adapted for the numeric integration of parabolic Partial Differential Equations (PDE) in one space dimension are applied. The semi-discrete system of ordinary differential equations in the time direction, obtained by applying the MOL to PDE, is solved with the use of a method of Adapted Series, based on Scheifele’s G-functions. This method integrates exactly unperturbed linear systems of ordinary differential equations, with only one G-function. An implementation of this algorithm is used to approximate the solution of two test problems proposed by various authors. The results obtained by the Dufort-Frankel, Crank-Nicholson and the methods of Adapted Series versus the analytical solution, show the results of mistakes made.展开更多
运用Mawhin重合度理论,讨论一类半直线上三阶多点边值问题(q(t)x″(t))′=f(t,x(t),x′(t),x″(t)),a.e.t∈[0,+∞);■(η■在dim Ker L=2共振情形下的可解性,获得了该边值问题至少存在一个解的充分条件.这里f:[0,1]×R^(3)→R满足L...运用Mawhin重合度理论,讨论一类半直线上三阶多点边值问题(q(t)x″(t))′=f(t,x(t),x′(t),x″(t)),a.e.t∈[0,+∞);■(η■在dim Ker L=2共振情形下的可解性,获得了该边值问题至少存在一个解的充分条件.这里f:[0,1]×R^(3)→R满足L^(1)[0,+∞)-Carathéodory条件,αi,βj∈R(1≤i≤m,1≤j≤n),0<ξ_(1)<ξ_(2)<…<ξ_(m)<+∞,0<η_(1)<η_(2)<…<η_(n)<+∞(m,n∈Z+),q(t)>0,q(t)∈C[0,+∞)∩C^(2)(0,+∞),1/q(t)∈L^(1)[0,+∞).展开更多
文摘Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.
基金National Natural Science Foundation of China(No.11271248)
文摘A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.
文摘We consider a Hilbert boundary value problem with an unknown parametric function on arbitrary infinite straight line passing through the origin. We propose to transform the Hilbert boundary value problem to Riemann boundary value problem, and address it by defining symmetric extension for holomorphic functions about an arbitrary straight line passing through the origin. Finally, we develop the general solution and the solvable conditions for the Hilbert boundary value problem.
文摘This paper investigates existence of positive solutions of singular sub-linear boundary value problems on a half-line. Necessary and sufficient conditions for the existence of positive continuous solutions or smooth solutions on [0, ∞] are given by constructing new lower and upper solutions.
基金Supported by the Fundamental Research Funds for the Central Universities (2011YXL044)the NNSF of China (11101385)
文摘In this paper, we are concerned with the existence of a second-order differential equation with m-point boundary conditions on the half line. The existence results are proved by the Leray-Scha¨uder point theorem in a special Banach space. Green function plays an important role in the proof and its discussion is very interesting. The results obtained generalize those in the previous references.
文摘We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems： additional edge singularities are known to develop in that case. This paper includes a rigorous error analysis proving the convergence of our numerical scheme. Three types of examples are covered： the Laplace equation in free space, the linear elasticity equation in free space, and in half space.
文摘The Method Of Lines (MOL) and Scheifele’s G-functions in the design of algorithms adapted for the numeric integration of parabolic Partial Differential Equations (PDE) in one space dimension are applied. The semi-discrete system of ordinary differential equations in the time direction, obtained by applying the MOL to PDE, is solved with the use of a method of Adapted Series, based on Scheifele’s G-functions. This method integrates exactly unperturbed linear systems of ordinary differential equations, with only one G-function. An implementation of this algorithm is used to approximate the solution of two test problems proposed by various authors. The results obtained by the Dufort-Frankel, Crank-Nicholson and the methods of Adapted Series versus the analytical solution, show the results of mistakes made.
文摘运用Mawhin重合度理论,讨论一类半直线上三阶多点边值问题(q(t)x″(t))′=f(t,x(t),x′(t),x″(t)),a.e.t∈[0,+∞);■(η■在dim Ker L=2共振情形下的可解性,获得了该边值问题至少存在一个解的充分条件.这里f:[0,1]×R^(3)→R满足L^(1)[0,+∞)-Carathéodory条件,αi,βj∈R(1≤i≤m,1≤j≤n),0<ξ_(1)<ξ_(2)<…<ξ_(m)<+∞,0<η_(1)<η_(2)<…<η_(n)<+∞(m,n∈Z+),q(t)>0,q(t)∈C[0,+∞)∩C^(2)(0,+∞),1/q(t)∈L^(1)[0,+∞).
