Existence of positive solutions for a class of higher-order nonlinear fractional differential equations with integral boundary conditions and a parameter

In this paper, we study the existence of positive solutions for a class of higher-order nonlinear fractional differential equations with integral boundary conditions and a parameter. By using the properties of the Green’s function, u ₀-positive function and the fixed point index theory, we obtain some existence results of positive solution under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The method of this paper is a unified method for establishing the existence of multiple positive solutions for a large number of nonlinear differential equations of arbitrary order with any allowed number of non-local boundary conditions.     

Positive solutions of higher-order nonlinear fractional differential systems with nonlocal boundary conditions

The paper deals with the existence and multiplicity of positive solutions for a system of higher-order nonlinear fractional differential equations with nonlocal boundary conditions. The main tool used in the proof is fixed point index theory in cone. Some limit type conditions for ensuring the existence of positive solutions are given.     

Multiple solutions to a three-point boundary value problem for higher-order ordinary differential equations

In this paper, we provide sufficient conditions for the existence of at least three solutions to a three-point boundary value problem for higher-order ordinary differential equations. The nonlinear term f in the differential equation under consideration may depend on higher-order derivatives of arbitrary order and this is where the main novelty of this work lies. By applying the two pairs of upper and lower solutions method of Henderson and Thompson, as well as degree theory, the existence of at least three solutions of the problem is given.     

Existence of positive solutions for a system of second-order m-point BVPs with variable parameters

In this paper, we study the existence of positive solutions for a class of second-order nonlinear m-point boundary value problems of differential system. By using the fixed point theory of cone expansion and compression with norm type, we show the sufficient conditions for the existence results.     

Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems

We investigate the existence and multiplicity of positive solutions of multi-point boundary value problems for systems of nonlinear higher-order ordinary differential equations.     

Positive solutions of four-point boundary value problems for higher-order p-Laplacian operator

In this paper, we study the existence of positive solutions for the nonlinear four-point singular boundary value problem for higher-order with p-Laplacian operator. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear singular boundary value problem with p-Laplacian operator are obtained.     

Analog of the first Fredholm theorem for higher-order nonlinear differential equations

We study the existence of solutions continuously depending on a parameter for higher-order nonlinear ordinary differential equations with linear boundary conditions. In particular, we prove a theorem of Fredholm type providing tests for the unique solvability of this problem.     

On a system of second-order multi-point boundary value problems

We study the existence of positive solutions for a system of nonlinear second-order ordinary differential equations subject to some multi-point boundary conditions. The nonexistence of positive solutions is also investigated.     

Positive solutions of a nonlinear impulsive equation with periodic boundary conditions

In this paper, we investigate nonlinear second order differential equations subject to linear impulse conditions and periodic boundary conditions. Sign properties of an associated Green’s function are exploited to get existence results for positive solutions of the nonlinear boundary value problem with impulse. Upper and lower bounds for positive solutions are also given. The results obtained yield periodic positive solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.     

Unbounded positive solutions of higher-order nonlinear functional differential equations

Classification schemes for positive solutions of a class of higher-order nonlinear functional differential equations are given in terms of their asymptotic behavior, and necessary as well as sufficient conditions for the existence of these solutions are also provided.     

Existence of multiple solutions of higher-order nonlinear elliptic equations

We study the existence of multiple solutions for a class of even-order nonlinear elliptic equations with the Dirichlet boundary conditions. We also study the corresponding nonlinear Hamiltonian system of higher-order linear equations.     

Three positive solutions for delay differential equation BVPs with p-Laplacian on infinite interval

In this paper we investigate the existence of three positive solutions for delay differential equation boundary value problem with p-Laplacian on infinite interval. By using the fixed point theorem in a cone introduced by Avery and Petereson, the existence of at least three positive solutions is obtained under suitable growth conditions imposed on the nonlinear term. As an application, one example is given to demonstrate our main result. To some extend, our paper complements and generalize the known results.     

Eigenvalue problems for higher-order p-Laplacian dynamic equations on time scales

Let T be a time scale. The existence of positive solutions for the nonlinear four-point singular boundary value eigenvalue problem with higher-order p-Laplacian dynamic equations on time scales is studied. By using the fixed-point index theory, we derive an explicit interval of λ such that for any λ in this interval, the existence of at least one positive solution to the eigenvalue problem is guaranteed, and the existence of at least two solutions for λ in an appropriate interval is also discussed.     

Positive solutions of m-point boundary value problems for a class of nonlinear fractional differential equations

This paper deals with the existence and multiplicity of positive solutions for a class of nonlinear fractional differential equations with m-point boundary value problems. We obtain some existence results of positive solution by using the properties of the Green’s function, u ₀-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator.     

二阶非线性微分方程组多点边值问题的正解

该文使用不动点指数理论,研究二阶奇异非线性微分方程组多点边值问题的正解和多个正解的存在性.给出某些保证解的存在性的极限条件,这些条件适用于较一般的函数.     

On positive solutions for a nonlinear boundary value problem with impulse

In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.     

Triple positive solutions for boundary value problems on infinite intervals

This paper deals with the existence of triple positive solutions for Sturm–Liouville boundary value problems of second-order nonlinear differential equation on a half line. By using a fixed point theorem in a cone due to Avery–Peterson, we show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term.     

二阶非线性q-差分微分方程两点边值问题两个迭代正解的存在性*

研究了二阶非线性q-差分微分方程两点边值问题,给出了系统两个正解存在的充分条件. 与其他文献中使用的不动点定理不同,文章不仅证明了该系统正解的存在性, 而且还利用单调迭代技巧给出了逼近正解的迭代格式.     

An existence and uniqueness criterion for solutions of boundary value problems

In this paper a technique is developed for the study of the existence and uniqueness of solutions to nth order ordinary differential equations satisfying n-point boundary conditions. Liapunov-like functions are employed to determine the existence and uniqueness of solutions to linear equations satisfying the boundary conditions, and these solutions are in turn used to determine existence for the general nonlinear case. A by-product of this technique is a matching technique for linear equations by which solutions of certain k-point boundary value problems (k < n) can be matched to extend the interval of existence for solutions to the n-point problem.     

MULTIPLE POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

This paper is concerned with the boundary value problem for a system of nonlinear third order differential equations. Under some suitable conditions, the existence and multiplicity of the positive solutions are established by using abstract fixed-point theorems.