Existence of solutions for nonlinear singular boundary value problems

Existence of solutions to the two-point boundary value problem (p(t)y')' = q(t)f(t, y,p(t)y'), y(l) = 0, lim_t→0+ p(t)y'(t) = 0 is established under a variety of conditions. Here p(0) = 0 is allowed, and q is not assumed to be continuous at 0, so the problem may be doubly singular. In addition, the Dirichlet problem for this differential equation is investigated     

n阶非线性常微分方程非线性k点边值问题解的存在性

利用格林函数和上下解方法讨论了n阶非线性常微分方程之几类具有非线性k点边界条件的边值问题的存在性。     

Two-point and three-point boundary value problems for n th-order nonlinear differential equations

In this article, we are concerned with existence and uniqueness of solutions of four kinds of two-point boundary value problems for nth-order nonlinear differential equations by “Shooting” method, and studied existence and uniqueness of solutions of a kind of three-point boundary value problems for nth-order nonlinear differential equations by “Matching” method.     

Existence of positive solutions of Lidstone boundary value problems

We show that there exists at least one positive solution for Lidstone boundary value problem

     

Nontrivial solutions of singular two-point boundary value problems with sign-changing nonlinear terms

The singular two-point boundary value problem

     

Positive solutions for systems of nonlinear discrete boundary value problems

Existence of eigenvalues yielding positive solutions for systems of second order discrete boundary value problems (two-point, three-point and generalized three-point) are established. The results are obtained by the use of a Guo–Krasnoselskii fixed point theorem in cones.     

Positive solutions of a nonlinear four-point boundary value problems in Banach spaces

In this paper, by using the fixed points of strict-set-contractions, we study the existence of at least one or two positive solutions to the four-point boundary value problem

     

Positive solutions for nonlinear singular boundary value problems

Some sufficient conditions for the existence of positive solutions to Dirichlet boundary value problems of a class of nonlinear second order differential equations are given.     

The method of fundamental solutions for elliptic boundary value problems

The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over the last three decades. Several applications of MFS-type methods are presented. Techniques by which such methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are also outlined. This revised version was published online in June 2006 with corrections to the Cover Date.     

Symmetric positive solutions of nonlinear boundary value problems

We study the nonlinear boundary value problem

     

一类具非线性边值条件的非线性方程的奇摄动问题

研究了一类具非线性边值条件的非线性方程的奇摄动问题,运用合成展开法构造了问题的形式渐近解,并用微分不等式理论证明了所得渐近解的一致有效性.     

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.     

An effective approach for numerical solution of linear and nonlinear singular boundary value problems

In this study, an effective approach is presented to obtain a numerical solution of linear and nonlinear singular boundary value problems. The proposed method is constructed by combining reproducing kernel and Legendre polynomials. Legendre basis functions are used to get the kernel function, and then the approximate solution is obtained as a finite series sum. Comparison of numerical results is made with the results obtained by other methods available in the literature. Furthermore, efficiency and accuracy of the method are demonstrated in tabulated results and plotted graphs. The numerical outcomes demonstrate that our method is very effective, applicable, and convenient.     

Existence of positive solutions for singular ordinary differential equations with nonlinear boundary conditions

We prove the existence of nonnegative solutions of the problem , , for a physically motivated class of nonlinearity . The results, which are established using a ``forbidden value' argument, are new even in the case of linear .

     

On existence of positive solutions of Sturm-Liouville boundary value problems for a nonlinear singular differential system

By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of Sturm-Liouville boundary value problems for a nonlinear singular differential system. Some well-known results in the literature are generalized and improved. An example is presented to illustrate the application of our main result.