Several Existence Theorems for Positive Radial Solutions to a Semilinear Elliptic BVP

The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.

A Generalized Existence Theorem of Backward Doubly Stochastic Differential Equations

In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.

Existence Theorem of Solutions for Mixed Variational Inequality in Banach Spaces

By using the property of generalized f-projection operator and FKKM theorem, the existence theorem of solutions for the mixed variational inequality is proved under weaker assumption in reflexive and smooth Banach space. The results improve and extend the corresponding results shown recentlv.

Existence of Multiple Positive Solutions for Fourth Order Two-point Boundary Value Problems

The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results.

EXISTENCE OF SOLUTIONS TO DIFFERENTIALINCLUSIONS IN BANACH SPACES

In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations between approximate solutions and solutions are studied. In the end ,the existence theorem of solutions to differential inclusions is obtained.

Existence of an Asymptotic Second-order Three-point Boundary Value Problem

By making use of degree theory, a new existence theorem is established for an asymptotic second-order three-point boundary value problem.

A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS

In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude （for example） existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES W^(m,p)t(Ω)

In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreomfor J(u) =0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.

FIfth-ORDER ISOTROPIC DESCARTES TENSOR

Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.

Nonlinear Riemann-Hilbert Problem for the First Order Elliptic System with the General Form

Nonlinear boundary problem for a class of the first order elliptic partial differential system with the general form are studied in this paper.And the equivalent nonlinear singular integral equations are established.Then the existence theorem of solution of the problem are also obtained.

Non-E_2 Class of Strongly Nonlinear Generalised R-H Boundary Value Problems for Second-Order Elliptic System

In this paper, a class of strongly non linear generalised Riemann Hilbert problems for second order elliptic system is studied. By means of the theory of integral equations and using an explicit form of the solution, a reduction is made to a nonlinear boundary value problem for two holomorphic functions. And using an approximation dealing with a solvable perturbed problems and suitable prior estimates, we prove that the problems possess solution in Hardy class, the solution w(z) belongs to W 1 2()∩W 2 p(G),p>2 .

Potential Method in the Theory of Thermoelasticity with Microtemperatures for Microstretch Solids

The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are given.The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established.The integral representation of general solutions is obtained.The existence of regular solutions of the BVPs is proved by means of the potential method(boundary integral method)and the theory of singular integral equations.

THEOREM OF EXISTENCE OF EXACT n LIMIT CYCLES FOR LINARD'S EQUATION

Liénard’s equation is a kind of important ordinary differential equations frequently appearing in engineering and technology, and hence receives great attention of many mathematicians. In 1949, H. J. Eckweiler conjectured that the equation +μsin+x=0 has infinite number of limit cycles. Then H. S. Hochstadt and B. Stephan, R. N. D’Heedene and others proved that this equation has at least n limit cycles in the interval |x|<(n+1)π for specified parameter μ. In 1980, Professor Zhang Zhifen proved that this equation has exact n limit cycles in the interval |x|<(n+1)π for any nonzero parameter μ, and thus pushed the related work forward greatly. In this paper, we shall prove that the Liénard’s equation has exact n limit cycles in a finite interval under a class of very general condition.

A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions

In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.

Approximate Weak Minimal Solutions of Set-Valued Optimization Problems

This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions are investigated.Some topological properties and existence theorems of these solutions are given.It is shown that for set-valued optimization problems with upper(outer)cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed.By using the polar cone and two scalarization processes,some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided.

Reflected Backward Doubly Stochastic Differential Equations with Discontinuous Coefficients

In this paper, we study one-dimensional reflected backward doubly stochastic differential equations （RBDSDEs） with one continuous barrier and discontinuous （left or right continuous） genera- tor. We obtain an existence theorem and a comparison theorem for solutions of the class of RBDSDEs.

Brill-Noether Theory for Rank Two Vector Bundles Generated by Their Sections

We here study the Brill-Noether theory for rank two vector bundles generated by their sections. We generalize the vanishing theorem, the Clifford theorem and the existence theorem to such bundles.

TWIN POSITIVE SOLUTIONS TO A CLASS OF NONLINEAR SECOND-ORDER THREE-POINTS BOUNDARY VALUE PROBLEMS

In this paper, we establish two existence theorems of twin positive solutions for a class of nonlinear second-order three-point boundary value problems, and concentrate on the case when nonlinear term does not satisfy usual conditions.

On Rational Functions with More than Three Branch Points

Let d be a positive integer and八be a collection of partitions of d of the form(a1,...,ap),(b1,...,bq),(m1+1,1,...,1),...,(m1+1,1,...,1),where(m1,...,ml)is a partition of p+g-2>0.We prove that there exists a rational function on the Riemann sphere with branch data ■ if and only if max(m1,...,ml)<d/GCD(a1,...,ap,b1,...bq),As an application,we give a new class of branch data which can be realized by Belyi functions on the Riemann sphere.

L^p SOLUTIONS TO BSDES WITH MONOTONIC AND UNIFORMLY CONTINUOUS GENERATORS

In this paper, we deal with Lp(p 】 1) solutions to one dimensional backward stochastic differential equations(BSDEs) with discontinuous(left or right continuous)generators. We obtain an existence theorem of Lpsolutions to BSDEs whose generators are discontinuous, monotonic in y and uniformly continuous in z.