Multiple fixed-sign solutions for a system of generalized right focal problems with deviating arguments

We consider the following system of generalized right focal boundary value problems

     

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.     

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     

On multiple fixed-sign solutions of a discrete system with Hermite boundary conditions

We consider the discrete system

     

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.     

Positive solutions for a singular fractional boundary value problem

We investigate the existence of positive solutions for a system of Riemann-Liouville fractional differential equations, supplemented with uncoupled nonlocal boundary conditions which contain various fractional derivatives and Riemann-Stieltjes integrals, and the nonlinearities of the system are nonnegative functions and they may be singular at the time variable. In the proof of our main theorems, we use the Guo-Krasnosel'skii fixed point theorem.     

Integral methods for computing solutions of a class of singular two-point boundary value problems

In this paper, we establish three iteration methods to compute solutions for a class of (weakly) singular two-point boundary value problems (xy^′)^′=f(x,y), where x(0,1) and <2. We obtain the sufficient conditions for existence of a unique solution on . Finally, we given some numerical examples.     

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.     

Sharp by order estimates of solutions of a simplest singular boundary value problem

We consider a boundary value problem ((0.1)) where f ∈ L_p (?), p ∈ [1, ∞] (L∞ (?) ? C (?)) and 0 ≤ q ∈ L^loc₁ (?). For a given p ∈ [1, ∞], for a correctly solvable problem (0.1) in L_p (?), we obtain minimal requirements to a positive, continuous function Θ(x) for x ∈ ? under which, regardless of f ∈ L_p (?), the solution y ∈ L_p (?) of problem (0.1) satisfies the equality . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Triple positive periodic solutions of nonlinear singular second-order boundary value problems

This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″(t) + λ(t)u(t) = f(t,u(t)),a.e.t ∈ [0,2π],u(0) = u(2π),u′(0) = u′(2π),where f(t,u) is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett–Williams and Krasnosel'skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.     

Twin solutions to singular boundary value problems

In this paper we establish the existence of two nonnegative solutions to singular and singular focal boundary value problems. Our nonlinearity may be singular at , and/or .

     

Positive solutions in the sense of distributions of singular boundary value problems

We obtain positive solutions in the sense of distributions of singular boundary value problems using perturbation and variational methods.

     

一类奇异边值问题正解的存在性

借助上下解方法和锥拉伸与锥压缩不动点定理研究了二阶非线性奇异边值问题u″ λf(t,u(t))=0,0相似文献   

Positive solutions for a system of second-order multi-point boundary value problems

In this paper, we present some results for positive solutions of a system of nonlinear second-order ordinary differential equations subject to multi-point boundary conditions.     

A necessary and sufficient condition for singular nonlinear second-order boundary value problems to have positive solutions

In this paper the following result is obtained: Suppose f(g,u,v) is nonnegative, continuous in (a, 6) ×R⁺ ×R ⁺ ; f may be singular at κ = a(and/or κ = b) and υ = 0; f is nondecreasing on u for each κ,υ,nonincreasing on υ for each κ,u; there exists a constant q ε (0,1) such that

Positive solutions for a system of second-order multi-point discrete boundary value problems

We present some results for positive solutions of a system of nonlinear second-order difference equations, subject to multi-point boundary conditions.     

Positive solutions for higher order multi-point boundary value problems with nonhomogeneous boundary conditions

We study nth order boundary value problems with a nonlinear term f(t,x) subject to nonhomogeneous multi-point boundary conditions. Criteria for the existence of positive solutions of such problems are established. Conditions are determined by the relationship between the behavior of f(t,x)/x near 0 and ∞ when compared with the smallest positive characteristic value of an associated linear integral operator. This work improves and extends some recent results in the literature for the second order problems. The results are illustrated with examples.     

出现在化学反应器理论中的奇摄动边值问题的渐近解

研究了一类出现在化学反应器理论中的奇摄动边值问题.在适当的条件下,用合成展开法构造出该问题的形式近似式,并应用微分不等式理论证明了解的存在性及其渐近性质.