Banach空间非线性脉冲积分方程解的存在性

利用Monch不动点定理和分段估计方法,本文研究Banach空间非线性脉冲积分方程解的存在性,但是我们不使用脉冲项的紧型条件和非紧型测度估计的限制性条件.作为一个应用,我们讨论Banach空间一阶非线性脉冲微分方程终值问题解的存在性.     

Banach空间非线性脉冲Hammerstein积分方程解的存在性

研究了Banach空间中定义在无穷区间R+上具有无穷多个脉冲点的Hammerstein积分方程解的存在性.利用MLnch不动点定理,建立了该类方程解的存在定理,并给出实例说明了该定理在无穷维脉冲积分方程组中的应用.     

一类非线性非紧算子不动点定理的推广及其应用

本文研究了一类非线性非紧算子不动点定理.利用锥理论,在不需要非线性项满足连续性和紧性条件下,获得无穷区间上Frodholm型积分方程解的存在唯一性,并给出逼近解迭代序列的误差估计.     

Banach空间中二阶非线性混合型脉冲微分-积分方程的解

利用一个比较结果和M(o)nch不动点定理,研究了Banach空间中二阶非线性混合型脉冲微分-积分方程初值问题解的存在性,推广了某些现有结果.     

无界域上一类非线性积分微分方程解的存在性

在比较宽松的条件下,研究了无界域上一类非线性积分微分方程解的存在性.通过引进等价的范数,利用递归法、Tonelii近似序列和局部凸拓扑,建立了新的存在性定理,改进了定义在有界域上的非线性湿气迁移方程的相应结果.     

关于抛物型积分-微分方程

本文应用 Galerkin 方法讨论一类无界区域上拟线性抛物型积分-微分方程初边值问题解的存在性,作为应用,我们得出了带吸咐项的非线性水动力弥散方程解的存在性定理。     

Banach空间一阶脉冲积分-微分方程初值问题解的存在性

利用M o。nch不动点定理和比较结果,研究了实Banach空间中一阶非线性脉冲微分-积分方程的初值问题解的存在性,本文对已有结果作了推广和改进.     

一个减算子不动点定理及其对非线性Volterra型积分方程的应用

利用锥理论,在不需要上下解的条件下,获得一个新的减算子不动点定理,推广了最近文献的结果;并给出Banach空间中非线性Volterra型积分方程解的唯一性.     

稳态Schr\"{o}dinger方程解的Liouville型定理

给出了锥中稳态Schr\"{o}dinger方程解的Liouville型定理, 推广了邓冠铁在半空间中关于拉普拉斯方程解的相关结论.     

一类非线性算子方程解的存在唯一性及其应用

该文在更广泛的条件下,利用锥理论和Banach压缩映象原理证明了序Banach空间中一类非线性算子方程解的存在唯一性定理,并应用到Banach空间中二阶非线性混合型微分积分方程初值问题,改进并推广了已有的一些结果.     

Existence of time periodic solutions for the 3-D viscous primitive equations of large-scale dry atmosphere

In this paper, we consider the existence of time periodic solutions of the 3-D viscous primitive equations of large-scale dry atmosphere. We used the Galerkin method. Firstly, by Leray-Schauder fixed point theorem, we prove the existence of approximate solutions of the primitive equations, then we show the convergence of the approximate solutions, and we also get the uniqueness to the primitive equations.     

Existence and Uniqueness of Solutions for Time-Fractional Oldroyd-B Fluid Equations with Generalized Fractional Derivatives

In this paper, we study the existence and uniqueness of solutions for time-fractional Oldroyd-B fluid equations with generalized fractional derivatives. We distinguish two cases. Firstly for the linear case, we get regularity results under some hypotheses of the source function and the initial data. Secondly for the nonlinear case, we use the Banach fixed point theorem to obtain the existence and uniqueness of solutions.     

Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators

We consider a system of nonlinear coupled equations involving magnetic Schrödinger operators and general potentials. We provide the criteria for the existence of multiple solutions to these equations. As special cases we get the classical results on existence of infinitely many distinct solutions within Hartree and Hartree–Fock theory of atoms and molecules subject to an external magnetic fields. We also extend recent results within this theory, including Coulomb system with a constant magnetic field, a decreasing magnetic field and a “physically measurable” magnetic field.     

Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions

This paper describes an application of Rota and collaborator’s ideas, about the foundation on combinatorial theory, to the computing of solutions of some linear functional partial differential equations. We give a dynamical interpretation of the convolution families of polynomials. Concretely, we interpret them as entries in the matrix representation of the exponentials of certain contractive linear operators in the ring of formal power series. This is the starting point to get symbolic solutions for some functional-partial differential equations. We introduce the bivariate convolution product of convolution families to obtain symbolic solutions for natural extensions of functional-evolution equations related to delta-operators. We put some examples to show how these symbolic methods allow us to get closed formulas for solutions of genuine partial differential equations. We create an adequate framework to base theoretically some of the performed constructions and to get some existence and uniqueness results.     

The Existence of Almost Periodic Solutions of Second Order Neutral Differential Equations with Piecewise Constant Argument

51.Intr0ducti0nInthispaper,weconsidertheexistenceofalmostperiodicsoluti0nsforthefoll0wingneutralfunctionaldifferentialebuationwithpiecewiseconstantargument:wherep,qarenonzeroconstants,p(t)lsanalmostper1odicfunctlon,g:RXRXR-Risanalm0stperiodicfunctionintanduniformlyonRXR,andL.jstandsforthegreatest-integerfunction.Notethatforanyintegern,if2n-10)andtheequations(1),(2)areadvanced(orretardedrespectively).Differentialequationswithpiecewiseconstantar…     

薛定谔方程及薛定谔-麦克斯韦方程的多解

不作周期性和对称性的假设,也没有Ambrosetti-Rabinowitz增长控制条件,我们得到了一类超线性薛定谔方程在全空间中无穷多解的存在性结果.同时,得到了一类超线性薛定谔-麦克斯韦方程无穷多解的存在性结果.     

Periodic and homoclinic solutions generated by impulses for asymptotically linear and sublinear Hamiltonian system

In this paper, we get the existence of periodic and homoclinic solutions for a class of asymptotically linear or sublinear Hamiltonian systems with impulsive conditions via variational methods. However, without impulses, there is no homoclinic or periodic solution for the system considered in this paper. Moreover, our results can be used to study the existence of periodic and homoclinic solutions of difference equations.     

Multibump solutions for discrete periodic nonlinear Schrödinger equations

In this paper, we study the existence of multibump solutions for discrete nonlinear Schrödinger equations with periodic potentials. We first reduce the existence of multibump homoclinic solutions to the existence of an isolated homoclinic solution with a nontrivial critical group. Then, we study the existence of homoclinics with nontrivial critical groups for both superlinear and asymptotically linear discrete periodic nonlinear Schrödinger equations, and we provide simple sufficient conditions for the existence of homoclinics with nontrivial critical groups in the positive definite case. As an application, we get, without any symmetry assumptions, infinitely many geometrically distinct homoclinic solutions with exponential decay at infinity.     

四阶非线性常微分方程非线性两点边值问题解的存在唯一性

本文利用Ｂｏｌｚａｎｏ定理，给出了四阶非线性常微微分方程具有非线性边界条件的两点边值问题（１）（２）２，（１）（２）３存在解与存在唯一解的一般性结果，并将所得结果应用于Ｌｉｐｓｃｈｉｚ方程，对Ｌｉｐｓｃｈｉｔｚ方程满足边界条件（２）２，（２）３的边值问题给出了存在解与存在唯一解的具体的充分条件。     

Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises

In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.