FREDHOLM DETERMINANT SOLUTION FOR NONLINEAR EQUATIONS ASSOCIATED WITH ISOSPECTRAL SCHRODINGER EICENVALUE PROBLEM

ＦＲＥＤＨＯＬＭＤＥＴＥＲＭＩＮＡＮＴＳＯＬＵＴＩＯＮＦＯＲＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮＳＡＳＳＯＣＩＡＴＥＤＷＩＴＨＩＳＯＳＰＥＣＴＲＡＬＳＣＨＲＯＤＩＮＧＥＲＥＩＣＥＮＶＡＬＵＥＰＲＯＢＬＥＭＨｕａｎｇＬｉｅｄｅ（黄烈德）；ＸｉａＺｈｏｎｇ...     

SYMMETRIES， BāCKLUND TRANSFORMATIONS AND BOUNDARY－INITIAL VALUE PROBLEMS FOR NONLINEAR CHROMATOGRAPH

ＳＹＭＭＥＴＲＩＥＳ，Ｂ■ＣＫＬＵＮＤＴＲＡＮＳＦＯＲＭＡＴＩＯＮＳＡＮＤＢＯＵＮＤＡＲＹ－ＩＮＩＴＩＡＬＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＣＨＲＯＭＡＴＯＧＲＡＰＨＹＥＱＵＡＴＩＯＮＷａｎｇＭｉｎｇｌｉａｎｇ（王明亮）（Ｄｅｐｔ．ｏ...     

POSITIVE SOLUTIONS AND BIFURCATION OF FULLY NONLINEAR ELLIPTIC EQUATIONS INVOLVING SUPER－CRITICAL SOBOLEV EXPONENTS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＯＦＦＵＬＬＹＮＯＮＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＩＮＶＯＬＶＩＮＧＳＵＰＥＲ－ＣＲＩＴＩＣＡＬＳＯＢＯＬＥＶＥＸＰＯＮＥＮＴＳ￥ＱＵＣＨＡＮＧＺＨＥＮＧ（屈长征）（Ｉｎｓ...     

ASYMPTOTIC BEHAVIOR OF NONOSCILLATORY SOLUTIONS OF A SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＮＯＮＯＳＣＩＬＬＡＴＯＲＹＳＯＬＵＴＩＯＮＳＯＦＡＳＥＣＯＮＤＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ（孟繁伟）曲阜师范大学，邮编：２７３１６５ＭｅｎｇＦａｎｗｅｉ（ＱｕｆｕＮ...     

EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTION FOR CERTAIN NONLINEAR DEGENERATE PARABOLIC SYSTEMS

ＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＧＬＯＢＡＬＳＯＬＵＴＩＯＮＦＯＲＣＥＲＴＡＩＮＮＯＮＬＩＮＥＡＲＤＥＧＥＮＥＲＡＴＥＰＡＲＡＢＯＬＩＣ　ＳＹＳＴＥＭＳＬＵＧＵＯＦＵ（卢国富）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｐｕｔｉ...     

NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

ＮＯＮＮＵＬＬＤＩＳＴＲＩＢＵＴＩＯＮＯＦＴＨＥＬＩＫＥＬＩＨＯＯＤＲＡＴＩＯＣＲＩＴＥＲＩＯＮＦＯＲＴＥＳＴＩＮＧＴＨＥＥＱＵＡＬＩＴＹＯＦＤＩＡＧＯＮＡＬＢＬＯＣＫＳＷＩＴＨＢＬＯＣＫＷＩＳＥＩＮＤＥＰＥＮＤＥＮＣＥＡ．Ｋ．Ｇｕｐｔａ；Ｃ．Ｃ．Ｃ...     

FORCED OSCILLATIONS OF HYPERBOLIC DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

ＦＯＲＣＥＤＯＳＣＩＬＬＡＴＩＯＮＳＯＦＨＹＰＥＲＢＯＬＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＤＥＶＩＡＴＩＮＧＡＲＧＵＭＥＮＴＳＣＵＩＢＡＯＴＯＮＧ（崔宝同）（ＢｉｎｚｈｏｕＮｏｒｍａｌＣｏｌｌｅｇｅ，Ｂｉｎｚｈｏｕ２５６６０４，Ｃ...     

EXISTENCE AND THE NUMBER OF PERIODIC SOLUTIONS ABOUT ONE CLASS DIFFERENTIAL EQUATION

ＥＸＩＳＴＥＮＣＥＡＮＤＴＨＥＮＵＭＢＥＲＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＡＢＯＵＴＯＮＥＣＬＡＳＳＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＦｅｎｇＺｈａｏｓｈｅｎｇ（冯兆生）（ＮｏｒｔｈｅｒｎＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，北方交通大学...     

THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＡＷＥＡＫＳＯＬＵＴＩＯＮＯＦＱＵＡＳＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＷＩＴＨＣＲＩＴＩＣＡＬＳＯＢＯＬＶＥＸＰＯＮＥＮＴＯＮＵＮＢＯＵＮＤＥＤＤＯＭＡＩＮＬｉＧｏｎｇｂａｏ（李工宝）（Ｉｎｓｔ．ｏｆＭａｔｈ...     

A NOTE OF UNIFORM EXPONENTIAL STABILIZATION FOR NONCONTRACTIVE SEMIGROUPS UNDER COMPACT PERTURBATION

ＡＮＯＴＥＯＦＵＮＩＦＯＲＭＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＺＡＴＩＯＮＦＯＲＮＯＮＣＯＮＴＲＡＣＴＩＶＥＳＥＭＩＧＲＯＵＰＳＵＮＤＥＲＣＯＭＰＡＣＴＰＥＲＴＵＲＢＡＴＩＯＮＳｏｎｇＧｕｏｚｈｕ（宋国柱）（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｎａｎｊｉｎｇ...     

On a Quasilinear Degenerate Parabolic Equation from Prandtl Boundary Layer Theory

The equation arising from Prandtl boundary layer theory $$\frac{\partial u}{\partial t} -\frac{\partial }{\partial x_i}\left( a(u,x,t)\frac{\partial u}{\partial x_i}\right)-f_i(x)D_iu+c(x,t)u=g(x,t)$$ is considered. The existence of the entropy solution can be proved by BV estimate method. The interesting problem is that, since $a(\cdot,x,t)$ may be degenerate on the boundary, the usual boundary value condition may be overdetermined. Accordingly, only dependent on a partial boundary value condition, the stability of solutions can be expected. This expectation is turned to reality by Kružkov's bi-variables method, a reasonable partial boundary value condition matching up with the equation is found first time. Moreover, if $a_{x_i}(\cdot,x,t)\mid_{x\in \partial \Omega}=a(\cdot,x,t)\mid_{x\in \partial \Omega}=0$ and $f_i(x)\mid_{x\in \partial \Omega}=0$, the stability can be proved even without any boundary value condition.     

On ground state of fractional $p$-Kirchhoff equation involving subcritical and critical exponential growth

In this paper, we concern the existence of nontrivial ground state solutions of fractional $p$-Kirchhoff equation $$\left\{\begin{array}{ll} m\left(\|u\|^p\right) [(-\Delta)_p^su+V(x)|u|^{p-2}u] =f(x,u) \quad\text{in}\, \mathbb{R}^N, \vspace{0.2 cm}\\ \|u\|=\left(\int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy +\int_{\mathbb{R}^N}V(x)|u|^pdx\right)^{\frac{1}{p}}, \end{array}\right.$$ where $m:[0,+\infty)\rightarrow [0,+\infty)$ is a continuous function, $(-\Delta)_p^s$ is the fractional $p$-Laplacian operator with $0相似文献   

Gradient Estimates for a Nonlinear Diffusion Equation on Complete Manifolds

This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation:u_t = △u +▽φ·▽u+a(x)uln u + b(x)u on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvature bounded below by- K(K ≥ 0),where φ is a C~2 function,a(x) and b(x) are C~1 functions with certain conditions.     

SPECTRAL SEQUENCES OF COHOMOLOGIES OF SINGULARITIES OF C∞ MAPPINGS

ＳＰＥＣＴＲＡＬＳＥＱＵＥＮＣＥＳＯＦＣＯＨＯＭＯＬＯＧＩＥＳＯＦＳＩＮＧＵＬＡＲＩＴＩＥＳＯＦＣ∞ＭＡＰＰＩＮＧＳＸＩＡＯＥＲＪＩＡＮＡｂｓｔｒａｃｔＴｗｏｓｐｅｃｔｒａｌｓｅｑｕｅｎｃｅｓａｒｅｄｅｆｉｎｅｄｒｅｓｐｅｃｔｉｖｅｌｙｆｏｒｃｏｈ...     

ON THE FEIGENBAUM＇S FUNCTIONAL EQUATION f^P （λx）=λf（x）

The author considers the Feigenbaum‘s functional equation f^P(λx)=λf(x) for each p≥2.The existence of even unimodal C^1 solutions to this equation is discussed and a feasible method to construct such solutions is given.     

ON TAYLOR'S CONJECTURE ABOUT THE PACKING MEASURES OF CARTESIAN PRODUCT SETS

1.IntroductionInthegeometryoffractals,Hausdorffmeasurealiddimensionplayaveryimportantrole.Olltheotherhand,therecelltilltroductionofpackingmeasureshasledtoagreaterunderstandillgofthegeometrictheoryoffractals,aspackingmeasuresbehaveillawnythatis'dual'toHausdoofmeasure8inmanyrespectsl2].Forexample,denotingHausdorffdimellsionandpackingdimensionbydimandDimrespectively,wehavedim(ExF)2dimE dimF,whileDim(ExF)5DimE DimF.Itiswell-kllowenthatifECRm,FCR",thenH(ExFW1T2)2b'H((E,W1)H(FW2)forsome…     

Well-Posedness of Solutions for Sixth-Order Cahn-Hilliard Equation Arising in Oil-Water-Surfactant Mixtures

In this paper, by using the $L_p$-$L_q$-estimates, regularization property of the linear part of $e^{-t\Delta^3}$ and successive approximations, we consider the existence and uniqueness of global mild solutions to the sixth-order Cahn-Hilliard equation arising in oil-water-surfactant mixtures in suitable spaces, namely $C^0([0,T];\dot{W}^{2,\frac{N(l-1)}2}(\Omega))$ when the norm $\|u_0\|_{\dot{W}^{2,\frac{N(l-1)}2}(\Omega)}$ is sufficiently small.     

Asymptotics of Analytic Semigroups,II

Let $T(\cdot)$ be an analytic $C_0$-semigroup of operators in a sector $S_{\theta}$, such that $||T(\cdot)||$ is bounded in each proper subsector $S_{\theta_0}$. Let $A$ be its generator, and let $D^{\infty}(A)$ be its set of $C^{\infty}$-vectors. It is observed that the (general) Cauchy integral formula implies the following extension of Theorem 5.3 in [1] and Theorem 1 in [4]: for each proper subsector $S_{\theta_0}$, there exist positive constants $M,\,\delta$ depending only on $\theta_0$, such that $(\delta^n/n!)||z^nA^nT(z)x||\leq M\,||x||$ for all $n\in\Bbb N,\, z\in S_{\theta_0}$, and $x\in D^{\infty}(A)$. It follows in particular that the vectors $T(z)x$ (with $z\in S_{\theta}$ and $x\in D^{\infty}(A)$) are analytic vectors for $A$ (hence $A$ has a dense set of analytic vectors).     

Infinite-dimensional porous media equations and optimal transportation

In this paper, we study a class of nonlinear diffusion equations in a Hilbert space X, $\partial_t\mu_t -\nabla\cdot\left(\nabla (L\circ\rho_t)\gamma\right)=0 \quad\mbox{\rm in}\,X\times(0,+\infty)$ with respect to a log-concave reference probability measure γ. We obtain existence, uniqueness and stability properties, in the framework of gradient flows in spaces of probability measures.     

On nonlinear wave equations with degenerate damping and source terms

In this article we focus on the global well-posedness of the differential equation , where is a sub-differential of a continuous convex function . Under some conditions on and the parameters in the equations, we obtain several results on the existence of global solutions, uniqueness, nonexistence and propagation of regularity. Under nominal assumptions on the parameters we establish the existence of global generalized solutions. With further restrictions on the parameters we prove the existence and uniqueness of a global weak solution. In addition, we obtain a result on the nonexistence of global weak solutions to the equation whenever the exponent is greater than the critical value , and the initial energy is negative. We also address the issue of propagation of regularity. Specifically, under some restriction on the parameters, we prove that solutions that correspond to any regular initial data such that , are indeed strong solutions.