Nontrivial Solutions of Semilinear Elliptic Equations Involving Critical Sobolev Exponents

ＮｏｎｔｒｉｖｉａｌＳｏｌｕｔｉｏｎｓｏｆＳｅｍｉｌｉｎｅａｒＥｌｌｉｐｔｉｃＥｑｕａｔｉｏｎｓＩｎｖｏｌｖｉｎｇＣｒｉｔｉｃａｌＳｏｂｏｌｅｖＥｘｐｏｎｅｎｔｓＨａｎＪｉａｎｌｏｎｇ（韩建龙）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｔｉａ...     

Some Results on Evolutionary Equations Involving Functions of the Eigenvalues of the Hessian

How to design the parabolic counterpart of the nonlinear elliptic equation involving function of the eigenvalues of the Hessian is discussed and the first initial-boundary value problem for such a parabolic equation is studied.     

Hölder Continuous Solutions to Complex Hessian Equations

We prove the Hölder continuity of the solution to complex Hessian equation with the right hand side in L ^p , \(p>\frac {n}{m}\) , 1 < m < n, in a m-strongly pseudoconvex domain in ? ⁿ under some additional conditions on the density near the boundary and on the boundary data.     

Regularity of Weak Solutions to a Class of Complex Hessian Equations on Kähler Manifolds

We prove the smoothness of weak solutions to a class of complex Hessianequations on closed Kähler manifolds, by use of the smoothing property of the corresponding gradient flow.     

Semicontinuity of Majorants and Minorants of Lyapunov’s Exponents as Functions of Complex Parameter

A parametric family of linear differential systems with continuous coefficients bounded on the semi-axis and analytically dependent on a complex parameter is considered. It is established that the majorant (minorant) of the Lyapunov exponent considered as a function of the parameter is upper (lower) semicontinuous.     

A System of Schrödinger Equations in the Critical Case

A system of nonlinear Schrödinger equations u _k } / t=ia _k u _k+f _k (u,u ^*), t>0, k=1,... ,m; u _k (0,x)=u _k0 (x), where f _k are homogeneous functions of order 1+4/n, is considered. Sufficient conditions for the globality of the solution are obtained. The existence of the explicit blow-up solution is proved.     

Second Order Complex Equations of Mixed Type

ＳｅｃｏｎｄＯｒｄｅｒＣｏｍｐｌｅｘＥｑｕａｔｉｏｎｓｏｆＭｉｘｅｄＴｙｐｅＳｕｎＨｅｓｈｅｎｇ（孙和生）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓ）Ｐ．Ｏ．Ｂｏｘ８００９，Ｂｅｉｊｉｎ...     

On the Solvability of Some Monge-Ampere Equations

This paper considers: (Ⅰ)M(u)≡det (D~2u) = f(x, u, Du) in W, u|w = g|δwHere f and g are smooth on W ×R×R~n and W respectively, f is positive, and gconvex. W is a uniformly convex domain.     

Generalized Poho?aev and Pucci-Serrin identities and non-existence results for p(x)-Laplacian type equations

In this article, generalizations of the well-known Pohožaev and Pucci-Serrin identities and (as consequences of them) some non-existence results for Dirichlet problems with p (x)-Laplacian are obtained.     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents北大核心CSCD

该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题。首先,由不动点原理,证明了问题解的局部存在性和唯一性。其次,利用上下解方法,给出在齐次Dirichlet边界条件下,问题的解在有限时间发生爆破的充分条件,即变指数大于零且初始值足够大,并对爆破时间的上下界进行了估计。     

Continuity of Some Classes of Functions Related to Degenerate Parabolic Equations and Its Applications

We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equations. Consequently, we prove that a function in such a class is continuous. As an application, we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form, including the anisotropic porous equations.     

A Kind of Partition Identity

Let σ(n) denote the set of partitions of n, usually denoted by 1~(k_1)2~(k_2)…n~(k_n) with k_1 2k_2 …nk_n. Let φ_i (t) (i=1,…, r) be power series in t (over comp lex field C) with positive radii of convergence and φ_i(0)=1.For every let the power-type generating function     

Periodic Orbits for Some Systems of Delay Differential Equations

We provide sufficient conditions for the existence of periodic orbits of some systems of delay differential equations with a unique delay. We extend Kaplan-Yorke＇s method for finding periodic orbits from a delay differential equation with several delays to a system of delay differential equations with a unique delay.     

Fractional Schrödinger Equations with Logarithmic and Critical Nonlinearities

Acta Mathematica Sinica, English Series - In this paper, we study a class of the fractional Schrödinger equations involving logarithmic and critical nonlinearities. By using the Nehari...     

Standing Waves of the Inhomogeneous Klein-Gordon Equations with Critical Exponent

This paper is concerned with the standing wave in the inhomogeneous nonlinear Klein- Gordon equations with critical exponent. Firstly, we obtain the existence of standing waves associated with the ground states by using variational calculus as well as a compactness lemma. Next, we establish some sharp conditions for global existence in terms of the characteristics of the ground state. Then, we show that how small the initial data are for the global solutions to exist. Finally, we prove the instability of the standing wave by combining the former results.     

Some Properties of Solutions for Some Types of Q-Difference Equations Originated from Q-Difference Painlevé Equation

In this paper, we mainly investigate some properties of meromorphic solutions for several q-difference equations, which can be seen as the q-difference analogues of Painlevé equations. Some results about the existence and the estimates of growth of meromorphic solution f for q-difference equations are obtained, especially for some estimates for the exponent of convergence of poles of ?_qf(z) := f(qz)-f(z), which extends some previous results by Qi and Yang.     

Solvability of Boundary Value Problems for Some Functional Differential Equations

This paper considers the following boundary value problems for functional differential equations: x' (t) = f(t, xt) (0相似文献