二阶差分边值问题的正解

本文研究了非线性项具有半正定和混合单调性的二阶差分边值问题正解的存在性.利用Krasnosel'skii不动点定理和锥拉伸与锥压缩不动点定理,讨论了二阶半正定非线性差分边值问题以及非线性项具有半正定和混合单调性的特征值问题正解的存在性,给出了这几类差分边值问题的正解存在性定理,改进和推广了具有正定非线性项的二阶差分边值问题的一些结果,并将所得结果应用于一个具体的二阶半正定非线性差分边值问题中.     

双锥不动点定理及其在非线性边值问题中的应用

本文研究了具可变号非线性项的非线性边值问题的正解存在性,推广了 Krasnoselskii 不动点定理,得到了新的锥上不动点定理,并应用这些定理给出这类边值问题正解的存在性．     

双锥不动点定理及其在非线性边值问题中的应用

本文研究了具可变号非线性项的非线性边值问题的正解存在性,推广了Krasnoselskii不动点定理,得到了新的锥上不动点定理,并应用这些定理给出这类边值问题正解的存在性.     

非线性分数微分方程解的若干存在性结论

研究了非线性分数微分方程解的存在性,通过考察非线性项在无穷远处的增长或者非线性项在某个有界集上的“高度”获得了若干新的存在性结论,主要工具是Schauder不动点定理和Leray-Schauder不动点定理．     

一类分数阶微分方程多点边值问题的多重正解

利用锥不动点等定理证明一类分数阶微分方程m点边值问题多重正解的存在性,应用Leray-Schauder非线性抉择定理和Guo-Krasnosel'skii不动点定理得到了边值问题(1)的多重正解的存在性.     

一类非线性二阶三点边值问题的解和正解

利用锥上的不动点定理,给出了非线性二阶三点边值问题解和正解的存在性定理.其中允许非线性项有一个负的下界.     

抽象空间中非线性算子方程变号解的存在性研究

利用Banach空间中的锥理论和不动点定理讨论了非线性算子方程变号解的存在性,给出了E_u_0空间下非线性算子方程变号解至少有一个变号解、一个正解和一个负解的条件,并讨论了仅通过一个上解条件得出非线性算子方程变号解的存在性定理.     

一类半正二阶三点边值问题的解和多解性

利用锥上的不动点定理,给出了非线性二阶三点边值问题解和多解的存在性定理.其中允许非线性项有一个负的下界.     

局部凸空间中一类非线性Volterra型积分方程解的存在性

首先利用局部凸空间非紧性测度得到一个新的不动点定理;并运用此定理研究了局部凸空间非线性V o lterra型积分方程解的存在性,然后应用到弱拓扑结构下对非线性V o lterra型积分方程解的存在性的讨论.推广了原有文献的结果.     

半正三阶三点边值问题正解的存在性

研究了一类非线性三阶三点边值问题解的存在性,在非线性项半正的情况下借助于Krasnoselskii锥拉伸与锥压缩不动点定理证明了正解的存在性.     

Existence of solutions of non-autonomous second order functional differential equations with infinite delay

In this paper the existence of solutions of a non-autonomous abstract retarded functional differential equation of second order with infinite delay is considered. Assuming the existence of an evolution operator corresponding to the associate abstract Cauchy problem of second order, we establish the existence of mild solutions of the functional equation. Furthermore, we study the existence of classical solutions of the abstract Cauchy problem of second order and we apply these results to establish the existence of classical solutions of the functional equation. Finally, we apply our results to study the existence of solutions of the non-autonomous wave equation with delay.     

Existence of solutions of the nonautonomous abstract Cauchy problem of second order

In this paper the existence of solutions of a nonautonomous abstract Cauchy problem of second order is considered. Assuming appropriate conditions on the operator of the equation, we establish the existence of mild solutions and, in some cases, we construct an evolution operator associated to the homogeneous equation. Using this evolution operator we obtain existence of solutions for the inhomogeneous equation. Finally, we apply our results to study the existence of solutions of the nonautonomous wave equation.     

一类非散度型非线性退化抛物方程解的存在性(英文)

In this paper, we discuss the existence of weak solutions to the initial and boundary value problem of a class of nonlinear degenerate parabolic equations in non-divergence form. Applying the method of parabolic regularization, we prove the existence of weak solutions to the problem. By carefully analyzing the approximate solutions to the problem, we make a series of estimates to the solutions and prove the weak convergence of the approximation solution sequence. Finally we testify the existence of weak solutions to the problem.     

Existence and multiplicity of positive solutions for singular quasilinear problems

In this work we combine perturbation arguments and variational methods to study the existence and multiplicity of positive solutions for a class of singular p-Laplacian problems. In the first two theorems we prove the existence of solutions in the sense of distributions. By strengthening the hypotheses, in the third and last result, we establish the existence of two ordered positive weak solutions.     

On the Existence of Solutions of Quasivariational Inclusion Problems

Quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of general vector ideal, proper, Pareto, weak quasioptimization problems, quasivariational inequalities, and vector quasiequilibrium problems. Further, we prove theorems on the existence for solutions of systems of these inclusions. As a corollary, we obtain an ideal minimax theorem concerning vector functions.     

On the solvability of a mathematical model for prion proliferation

We show that a model describing the interaction between normal and infectious prion proteins admits global solutions. More precisely, supposing the involved degradation rates to be bounded, we prove global existence and uniqueness of classical solutions. Based on this existence theory, we provide sufficient conditions for the existence of global weak solutions in the case of unbounded splitting rates. Moreover, we prove global stability of the disease-free steady state.     

Quasiperiodic solutions for nonlinear differential equations of second order with symmetry

In this paper, we study the existence of quasi-periodic solutions and the boundedness of solutions for a wide class nonlinear differential equations of second order. Using the KAM theorem of reversible systems and the theory of transformations we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.     

Periodic Solutions of Classical Hamiltonian Systems without Palais-Smale Condition

In this paper, we study the existence of periodic solutions for classical Hamiltonian systems without the Palais-Smale condition. We prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions. Moreover, we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function V.     

Traveling wave solutions in a delayed lattice competition-cooperation system

In this paper, we first reduce the existence of traveling wave solutions in a delayed lattice competition-cooperation system to the existence of a pair of upper and lower solutions by means of Schauder’s fixed point theorem and the cross iteration scheme, and then we construct a pair of upper and lower solutions to obtain the existence and nonexistence of traveling wave solutions. We also consider the asymptotic behaviour of any nonnegative traveling wave solutions at negative infinity.     

一类半线性双温度热传导方程整体强解的存在性

给出了一类半线性双温度热传导方程的初边值问题整体强解的存在条件,利用位势井方法证明了整体强解的存在性定理,且证明了方程的解或解对X的某些导数的L^2模估计式．