Constant-sign solutions of systems of higher order boundary value problems with integrable singularities

We consider some systems of boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using the Schauder fixed point theorem, we establish criteria such that the systems of boundary value problems have at least one constant-sign solution.     

Nontrivial solutions of singular nonlinear m-point boundary value problems

In this paper, by using the method of topology degree, some existence theorems of nontrivial solutions for singular nonlinear m-point boundary value problems are established. Our nonlinearity may be singular in its dependent variable.     

Positive solutions of singular third-order three-point boundary value problems

The positive solutions of a class of singular third-order three-point boundary value problems are considered by using the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type. In this class of problems, the nonlinear term is allowed to be singular. Main results show that this class of problems can have n positive solutions provided that the conditions on the nonlinear term on some bounded sets are appropriate.     

Positive solutions for singular m-point boundary value problems with positive parameter

In this paper, some new existence results for positive solutions for a class of singular m-point boundary value problems with parameter be obtained.     

Existence of solutions to derivative-dependent,nonlinear singular boundary value problems

This article examines two-point boundary value problems (BVPs) for second-order, singular ordinary differential equations where the right-hand-side of the differential equation may depend on the derivative of the solution. We introduce a method to obtain a priori bounds on all potential solutions, including their “derivatives”, to the singular BVP under consideration. The approach is based on the application of differential inequalities of singular type. The ideas are then applied to yield new existence results for solutions.     

A Calculus of Boundary Value Problems in Domains with Non–Lipschitz Singula Points

The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.     

一维p-Laplacian方程奇异边值问题的正解

本文讨论了一维p-Laplacian方程奇异边值问题的正解的存在性,其中函数f(t,x)可能在t=0,1都有奇点     

一类四阶奇异边值问题的正解

本文讨论了如下四阶奇异边值问题正解的存在性(?)其中p可能在t=0,1都有奇点.     

奇异差分边值问题上下解方法的推广

This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.     

Cubic spline solution of singularly perturbed boundary value problems with significant first derivatives

We develop a numerical technique for a class of singularly perturbed two-point singular boundary value problems on an uniform mesh using polynomial cubic spline. The scheme derived in this paper is second-order accurate. The resulting linear system of equations has been solved by using a tri-diagonal solver. Numerical results are provided to illustrate the proposed method and to compared with the methods in [R.K. Mohanty, Urvashi Arora, A family of non-uniform mesh tension spline methods for singularly perturbed two-point singular boundary value problems with significant first derivatives, Appl. Math. Comput., 172 (2006) 531–544; M.K. Kadalbajoo, V.K. Aggarwal, Fitted mesh B-spline method for solving a class of singular singularly perturbed boundary value problems, Int. J. Comput. Math. 82 (2005) 67–76].     

Singular problems motivated from classical upper and lower solutions

General existence criteria are presented for nonlinear singular boundary value problems. Our nonlinearity may be singular in both the dependent and independent variable. This revised version was published online in June 2006 with corrections to the Cover Date.     

Nontrivial solutions for higher-order m-point boundary value problem with a sign-changing nonlinear term

This paper studies the existence of nontrivial solutions for a class of higher-order m-point singular boundary value problems based on the topological degree of a completely continuous field, the first eigenvalue and its corresponding eigenfunction of a special linear operator. The nonlinear term in the boundary value problems is sign-changing and may be unbounded from below.     

Exact solutions of a class of second-order nonlocal boundary value problems and applications

In this paper, solutions of a class of second-order differential equations with some multi-point boundary conditions are studied. We give exact expressions of the solutions for the linear m-point boundary problems by the Green’s functions. As applications, we study uniqueness and iteration of the positive solutions for a nonlinear singular second-order m-point boundary value problem.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.     

Positive solutions of singular Caputo fractional differential equations with integral boundary conditions

In this paper, we investigate the existence of positive solutions of singular super-linear (or sub-linear) integral boundary value problems for fractional differential equation involving Caputo fractional derivative. Necessary and sufficient conditions for the existence of C³[0, 1] positive solutions are given by means of the fixed point theorems on cones. Our nonlinearity f(t, x) may be singular at t = 0 and/or t = 1.     

Existence and Uniqueness of Solutions to Singular Higher Order Two-point BVPs on Time Scales

This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method.The theorems obtained are very general.For the different time scale,the problem may be the corresponding continuous or discrete boundary value problem.     

奇异非线性边值问题的经典Agarwal-O'Regan方法

改进了奇异非线性边值问题的经典Agarwal-O'Regan方法.利用这个改进的方法建立了奇异非线性(p,n-p)共轭边值问题正解的局部存在性与多解性,其中允许非线性项关于时间和空间变元同时奇异.主要工具是锥拉伸与锥压缩型的Guo-Krasnosel'skii不动点定理和精确先验估计技巧.特别的,考察了非自治奇异非线性二阶、三阶、四阶共轭边值问题.     

Functional dependence and boundary-value problems with families of solutions

A linear Hamiltonian system Jy′ = (λA + B) y is considered on an open interval (a, b), where both a and b are singular. The system is assumed to be of limit point or limit circle type at the endpoints. A theory of boundary problems for such systems is developed. Explicit boundary conditions are given, resolvent operators constructed and unique solutions established. The results given extend to Hamiltonian systems a theory of singular boundary value problems due to M. H. Stone and K. Kodaira.     

Cubic spline for a class of singular two-point boundary value problems

In this paper we have presented a method based on cubic splines for solving a class of singular two-point boundary value problems. The original differential equation is modified at the singular point then the boundary value problem is treated by using cubic spline approximation. The tridiagonal system resulting from the spline approximation is efficiently solved by Thomas algorithm. Some model problems are solved, and the numerical results are compared with exact solution.     

POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER

Some results of existence of positive solutions for singular boundary value problems{-u"(t)=p(t)f(u(t)), t∈(0,1), u(0)=u(1)=0are given, where the function p(t) may be singular at t = 0, 1.