A Nonlinear Diffusion System with Coupled Nonlinear Boundary Flux

This paper studies a nonlinear diffusion system with coupled nonlinear boundary flux and two kinds of inner sources （positive for the first and negative for the second）, where the four nonlinear mechanisms are described by eight nonlinear parameters. The critical exponent of the system is determined by a complete classification of the eight nonlinear parameters, which is represented via the characteristic algebraic system introduced to the problem.     

SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY

In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [G. Bonanno and P. Candito, Appl.Anal., 88(4)(2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.     

BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS

In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.     

POSITIVE SOLUTIONS TO AN INTEGRAL BOUNDARY VALUE PROBLEM WITH DELAY

In this paper, we study a second order integral boundary value problem with delay. By the Krasnoselskii fixed point theorem, we obtain sufficient conditions for the existence of at least one or two positive solutions to the problem.     

GLOBAL BLOW-UP FOR A LOCALIZED DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS

This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain {0, a}, including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case.     

EXISTENCE OF MULTIPLE SOLUTIONS TO A FRACTIONAL DIFFERENCE BOUNDARY VALUE PROBLEM WITH PARAMETER

By establishing the corresponding variational framework, and using critical point theory, we give the existence of multiple solutions to a fractional difference boundary value problem with parameter. Under some suitable assumptions we obtain some results which ensure the existence of well precise interval of parameter for which the problem admits multiple solutions.     

Boundary Homogenization in the Spontaneous Potential Well-Logging

Motivated by the study on the spontaneous potential well-logging, this paper deals with the homogenization of boundary conditions for a class of elliptic problems with jump interface conditions.     

POSITIVE SOLUTIONS TO A NONHOMO- GENEOUS NONAUTONOMOUS SECOND- ORDER BOUNDARY VALUE PROBLEM

The existence of multiple positive solutions is studied for a nonlinear nonauto- nomous second-order boundary value problem with nonhomogeneous boundary con- ditions. In order to describe the growth behaviors of nonlinearity on some bounded sets, two height functions are introduced. By considering the integrals of the height functions and applying the Krasnosel＇skii fixed point theorems on a cone, several new results are proved.     

EXISTENCE OF THREE SOLUTIONS TO NONLINEAR DISCRETE DIRICHLET PROBLEM INVOLVING p-LAPLACIAN

In this paper, we study a nonlinear Dirichlet boundary value problem for difference equations involving the p-Laplacian with two positive parameters. One result on the existence of at least three solutions for this problem is obtained using critical point theory.     

EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR ONE-DIMENSIONAL p-LAPLACIAN

We study the existence of positive solutions to boundary value problems for one- dimensional p-Laplacian under some conditions about the first eigenvalues correspon- ding to the relevant operators by the fixed point theory. The main difficulties are the computation of fixed point index and the subadditivity for positively 1-homogeneous operator.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO FRACTIONAL BOUNDARY VALUE PROBLEMS

In this paper, using fixed point theorems of general β-concave operators in ordered Banach space, we obtain the existence and uniqueness of positive solutions to a class of fractional boundary problem. In the end, an example is given to illustrate our main result.     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETER

In this paper, we consider a class of nonlinear fractional differential equation boun- dary value problem with a parameter. By some fixed point theorems, sufficient con- ditions for the existence, nonexistence and multiplicity of positive solutions to the system are obtained. An example is given to illustrate the main results.     

STARLIKENESS AND SUBORDINATION PROPERTIES OF A LINEAR OPERATOR

In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator Lαk. For functions in this class Hαk(p, λ; h) we estimate the coefficients.Furthermore, some subordination properties related to the operator Lαkare also derived.     

THE CAUCHY PROBLEM OF THE HARTREE EQUATION

In this paper, we systematically study the wellposedness, illposedness of the Hartree equation, and obtain the sharp local wellposedness, the global existence in Hs, s≥1 and the small scattering result in Hs for 2 〈γ〈 n and s ≥ 2/γ - 1. In addition, we study the nonexistence of nontrivial asymptotically free solutions of the Hartree equation.     

The complexity and randomness of linear multi-secret sharing schemes with non-threshold structures

In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi- secret sharing scheme is measured by means of the complexity a and the randomness . Informally, the com- plexity a is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness is the ratio between the amount of information distributed to the set of users U = {1, …, n} and the minimum of information corresponding to every key. In this paper, we discuss a and of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make a and to be the minimum, respectively. That is, they are optimal.     

APPROXIMATE CONTROLLABILITY OF THE STOKES EQUATIONS WITH BOUNDARY CONDITION ON THE PRESSURE

In this paper, some properties of three-dimensional Stokes equations with boundary condition of pressure on parts of boundary are studied. By use of these properties, approximate controllability by tangent boundary controls acting on a subboundary is studied. In addition, the controllability problem is considered when its controls act on a subdomain.     

On Global Smooth Solution of A Semi-Linear System of Wave Equations in IR^3

In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the system for subcritical case by using conservation of energy and Strichartz＇s estimate. On the basis of Morawetz-Pohozev identity, we obtain the same result for the critical case.     

NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS

Let(E, ξ) = ind(En, ξn) be an inductive limit of a sequence(En, ξn)n∈N of locally convex spaces and let every step(En, ξn) be endowed with a partial order by a pointed convex(solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces,the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence(Sn)n∈N of ordering cones is nonconflicting, an existence theorem on lastingly weakly efficient points is presented. From this,an existence theorem on lastingly globally properly efficient points is deduced.     

An Image Denoising-Deblurring Adaptive Variational Problem in BV Space

In this paper, we establish the existence and uniqueness of a BV solution to an initial boundary value problem for a nonlinear integro-differential equation, which is related to a denoising and deblurring variational model in image restoration. Several experiments relevant to the restoration model are performed and numerical results are discussed.     

Modified Boussinesq System with Variable Coefficients： Classical Lie Approach and Exact Solutions

The Lie-group formalism is applied to investigate the symmetries of the modified Boussinesq system with variable coefficients. We derived the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The reduced systems of ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.