Nonlinear Riemann - Hilbert Problems without Transversality

Nonlinear Riemann - Hilbert problems (RHP) generalize two fundamental classical problems for complex analytic functions, namely: 1. the conformal mapping problem, and 2. the linear Riemann - Hilbert problem. This paper presents new results on global existence for the nonlinear (RHP) in doubly connected domains with nonclosed restriction curves for the boundary data. More precisely, our nonlinear (RHP) is required to become ?at infinity”?, i.e., for solutions having large moduli, a linear (RHP) with variable coefficients. Global existence for q-connected domains was already obtained in [9] for the special case that the restriction curves for the boundary data ?at infinity”? coincide with straight lines corresponding to linear (RHP)-s with special so-called constant - coefficient transversality boundary conditions. In this paper, the boundary conditions are much more general including highly nonlinear conditions for bounded solutions in the context of nontransversality. In order to prove global existence, we reduce the problem to nonlinear singular integral equations which can be treated by a degree theory of Fredholm - quasiruled mappings specifically constructed for mappings defined by nonlinar pseudodifferential operators.     

一类带非线性边界条件的非线性抛物方程的解的整体存在性

该文考虑带非线性边界条件的非线性抛物方程的正整体解的存在性与非存在性。通过使用上下解技巧，得到了所有正解整体存在的充分必要条件。作者所构造的上下解具有相同的形式且计算简便。     

n阶非线性常微分方程的非线性两点边值问题

本文利用打靶法,给出了ｎ阶非线性常微分方程具有非线性两点边界条件的边值问题存在解与存在唯一解的一般性结果,并将所得结果应用于Ｌｉｐｓｃｈｉｔｚ方程的两点过值问题,给出了存在解与存在唯一解的具体的充分条件。     

EXISTENCE AND NON-EXISTENCE OF GLOBAL SOLUTIONSOF A DEGENERATE PARABOLIC SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS＊

In this paper, we study the non-negative solutions to a degenerate parabolic system with nonlinear boundary conditions in the multi-dimensional case.By the upper and lower solutions method, we give the conditions on the existence and non-existence of global solutions.     

一类非线性Schr(o)dinger方程的整体小解

本文研究带有非线性项|u|~pu的高阶非线性Schr(?)dinger方程的Cauchy问题．对于p的某一取值范围。我们证明了此问题整体解的存在唯一性,并得到了解关于初值的连续依赖性及解具有较强的衰减估计。     

Convective Porous Medium Systems with Nonlinear Forcing at the Boundary

This paper deals with the global positive solutions of convective porous medium systems with nonlinear forcing at the boundary. Necessary and sufficient conditions on the global existence of all positive solutions are obtained.     

Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

In this paper we present existence results for solutions of nonlinear second-order boundary value problems with impulses. Our impulses are applied at p points in the interval and given implicitly by nonlinear functions of the solution. Moreover we allow functional dependence on the solution. Our existence results follow from the existence of a pair of well ordered lower and upper solutions. We generalize earlier results of Cabada and Tomec?ek, allowing more general compatible boundary conditions, impulses and φ-Laplacian equations.     

Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions.     

Upper and Lower Solution Methods for Fully Nonlinear Boundary Value Problems

Sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions. The conditions assume the existence of a strong upper solution-lower solution pair, a concept that is defined in the paper. The differential equation has nonlinear dependence on all lower order derivatives of the unknown; in particular, appropriate Nagumo conditions are obtained and employed.     

一类二阶非线性常微分方程非线性边界条件的两点边值问题

本文讨论了一类二阶非线性常微分方程之具有线性边界条件的和具有非线性边界条件的两点边值问题解的存在性.     

非线性Schr{odinger方程的初边值问题

本文证明了非线性Schrodinger方程的初值问题的H^S-解（1＜s≤2）的存在唯一性结果。     

边界耦合的牛顿渗流方程组解的整体存在与爆破

本文研究了由边界条件耦合的多维牛顿渗流方程组解的长时间行为.利用构造的多种上下解,得到了整体存在临界曲线与Fujita临界曲线.     

一类非线性Schr(o)dinger方程的整体自相似解

本文应用调和分析的方法研究了一类非线性Sehrodinger方程Cauchy问题整体自相似解的存在唯—性．     

一类带非局部源项的p-Laplace方程解的整体存在与爆破

本文研究一类在Neumann边值条件下带局部源项的p-Laplace方程解的整体存在和爆破性.利用微分不等式技巧,通过构造辅助函数的方法,获得了方程的解整体存在和解在有限时间爆破的充分条件,以及爆破时间的上下界估计,推广了相关文献结论.     

Global Solution for Quasilinear Wave Equations with Viscosity and Nonlinear Perturbation

1 IntroductionIn this paper we study globaJ solutions to the initiaLboundary value prob1em for quasilinearwave equations with viscosity and a nonlinear perterbation of the fOrmwhere fl is a bounded domain in RN with smooth boundarY afl, and the norilineax termsa(vp), g(u) axe like a(vp) = (l + )vlP)--'/P(P > 1), g(u) =--ju1"u.This problem describes the motion of fixed membrane with strong viscosity. The globalexistence and stability Of smooth solutions fOr one space dimensional case N = 1…     

Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions

This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions.For the heat diffusion case,the necessary and sufficient conditions on the global existence of all positive solutions are obtained.For the general fast diffusion case,we get some conditions on the global existence and nonexistence of positive solutions.The results of this paper fill the some gaps which were left in this field.     

Nonlinear Degenerate Parabolic Equation with Nonlinear Boundary Condition

In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive （weak） solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition.     

三阶奇摄动非线性边值问题

利用微分不等式理论,研究了某一类三阶奇摄动非线性边值问题。以二阶边值问题的已知结果为基础,引入Volterra型积分算子,建立了三阶非线性边值问题的上下解方法。在适当条件下,构造出具体的上下解,得出解的存在性和渐进估计。结果表明这种技巧也为三阶奇摄动边值问题的研究提出了崭新的思路。最后举例验证文中定理的正确性。     

一阶脉冲泛函微分方程非线性边值问题

考虑一阶脉冲泛函微分方程非线性边值问题,利用上下解方法和单调迭代技术得到了耦合解和唯一解存在的充分条件.所得结果改进和推广了文献的相关结果.     

n阶非线性微分方程的非线性三点边值问题

本文利用广义对接方法,建立了n阶非线性微分方程y(n)=f(x,y,y',…, y(n-1))满足非线性三点边界条件的非线性三点边值问题解的存在性与唯一性定理,所得结果将已有的很多相应结果作为特例.