Fixed point theorems for mixed monotone operators with perturbation and applications to fractional differential equation boundary value problems

The purpose of this paper is to present some new fixed point theorems for mixed monotone operators with perturbation by using the properties of cones and a fixed point theorem for mixed monotone operators. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.     

Fixed points of mixed monotone operators for existence and uniqueness of nonlinear fractional differential equations

In this paper we study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems by using new fixed point results of mixed monotone operators on cones.     

On nonlinear two-point boundary value problems for impulsive differential-algebraic problems

In this paper, we investigate boundary value problems for first order impulsive differential-algebraic problems with causal operators. Note that a corresponding boundary condition is given by a nonlinear function. Using a monotone iterative method we formulate general sufficient conditions under which such problems have solutions (extremal or a unique). An example shows that corresponding assumptions are satisfied. The results are new.     

Nonlinear boundary value problems for second order differential inclusions

In this paper, we study a class of nonlinear value boundary problems for second order differential inclusions with nonlinear perturbations, which satisfy the generalized Hartman condition weaker than that considered in some papers. Using techniques from multivalued analysis, theory of monotone operators and fixed points, we prove the existence of solutions in both “convex” and “nonconvex” cases. Our framework can be incorporated with Dirichlet, Neumann, and mixed boundary problems.     

Positive solutions to periodic boundary value problems involving nonlinear operators of Meir-Keeler-type

We establish fixed point theorems for mixed monotone operators of Meir-Keeler type on ordered Banach spaces through projective metric. As applications, we use the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for different classes of nonlinear problems which include two-order two-point boundary value problems and fourth-order two-point boundary value problems for elastic beam equations.     

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.     

Nonlinear boundary value problems

In this paper we consider two quasilinear boundary value problems. The first is vector valued and has periodic boundary conditions. The second is scalar valued with nonlinear boundary conditions determined by multivalued maximal monotone maps. Using the theory of maximal monotone operators for reflexive Banach spaces and the Leray-Schauder principle we establish the existence of solutions for both problems.     

奇异非线性四阶微分方程边值问题正解的存在唯一性

利用一类混合单调算子的一个不动点定理,给出了奇异非线性四阶微分方程边值问题的解的存在及惟一性.     

奇异二阶连续和离散边值问题正解的存在唯一性

利用一类混合单调算子的一个不动点定理,给出了奇异二阶微分方程边值问题和奇异二阶差分方程边值问题的解的存在及惟一性.     

Boundary value problems with causal operators

In this paper, we apply the monotone iterative method for nonlinear two-point boundary value problems with causal operators. We formulate sufficient conditions under which such problems have extremal or quasisolutions in a corresponding sector. We also investigate differential inequalities.     

奇异P-Lapace差分方程边值问题正解的存在唯一性

利用混合单调算子不动点定理研究了一维非线性奇异P-Lapace差分方程边值问题,得到P-Lapace差分方程边值问题的存在唯一正解的充要条件.     

二阶带时标的非线性奇异动力方程的m点边值问题的正解

研究二阶带时标的非线性奇异动力方程m点边值问题的正解,利用锥上的混合单调不动点定理,得到了正解的存在性和唯一性.本文中方程的非线性项可能是奇异的.并举例说明相应的结果.     

Monotone schemes for a class of nonlinear elliptic and parabolic problems

We construct monotone numerical schemes for a class of nonlinear PDE for elliptic and initial value problems for parabolic problems. The elliptic part is closely connected to a linear elliptic operator, which we discretize by monotone schemes, and solve the nonlinear problem by iteration. We assume that the elliptic differential operator is in the divergence form, with measurable coefficients satisfying the strict ellipticity condition, and that the right-hand side is a positive Radon measure. The numerical schemes are not derived from finite difference operators approximating differential operators, but rather from a general principle which ensures the convergence of approximate solutions. The main feature of these schemes is that they possess stencils stretching far from basic grid-rectangles, thus leading to system matrices which are related to M-matrices.     

Banach空间二阶非线性积分-微分方程组两点边值问题

直接利用混合单调迭代法,研究了Banach空间二阶非线性积分-微分方程组两点边值问题解的存在性.     

Periodic boundary value problems for second-order impulsive integro-differential equations

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for second-order nonlinear impulsive integro-differential equations of mixed type.     

New existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation

In this paper, we obtain some new and general existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation, which extend the corresponding results in [Z.T. Zhang, New fixed point theorems of mixed monotone operators and applications, J. Math. Anal. Appl. 204 (1996) 307-319, Theorem 1, Corollaries 1 and 2]. Moreover, some applications to nonlinear integral equations on unbounded region are given.     

Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems

Both linear and nonlinear singularly perturbed two point boundary value problems are examined in this paper. In both cases, the problems have a boundary turning point and are of convection-diffusion type. Parameter-uniform numerical methods composed of monotone finite difference operators and piecewise-uniform Shishkin meshes, are constructed and analyzed for both the linear and the nonlinear class of problems. Numerical results are presented to illustrate the theoretical parameter-uniform error bounds established.     

含有广义p-Laplace算子的非线性边值问题解的存在性的研究

该文研究了两类含有广义p-Laplace算子的非线性边值问题. 首先, 利用变分不等式解的存在性的结果, 证明了含有广义p-Laplace算子的非线性Dirichlet边值问题解的存在性. 然后, 提出了一类含有广义p-Laplace算子的非线性Neumann边值问题. 通过深入挖掘这两类非线性边值问题间的关系, 借助于极大单调算子值域的一个扰动结果, 证明了含有广义p-Laplace算子的非线性Neumann边值问题解的存在性. 文中采用了一些新的证明技巧,推广和补充了作者以往的一些研究工作.     

混合单调算子的两点拉伸型不动点定理

本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究.     

二阶混合单调型脉冲微分方程的初值问题

利用混合单调凝聚算子的耦合不动点定理,给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。