L—Estimates for the Gradient of Weak Solutions to a Class of Degenerate Nonlinear Elliptic Systems

We call that λ(x)belongs to Muckenhoupt class A_p if λ(x)≥0 and satisfiesfor all balls in R,where|B_R| denotes the Lebesgue measure of a ball with centerx_0 and radius R,andLet be a bounded domain.Define normHere,denotes the Banach space of all measurable functions defined on     

On Singular Dirichlet Problems for Semilinear Elliptic Equation of Second Order Ⅱ

ＯｎＳｉｎｇｕｌａｒ　ＤｉｒｉｃｈｌｅｔＰｒｏｂｌｅｍｓｆｏｒＳｅｍｉｌｉｎｅａｒ　ＥｌｌｉｐｔｉｃＥｑｕａｔｉｏｎｏｆＳｅｃｏｎｄＯｒｄｅｒⅡＺｈａｎｇＺｈｉｊｕｎ（张志军）（ＤｅｐａｒｔｍｅｎｔｏｆＭｏｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｗｅｓｔＮｏｒ...     

On the Multiple Solutions of Dirichlet Problems for semilinear Elliptic Equations (Critical Increasing Case)

In this paper we study Dirichlet problem:     

The Generalized Hölder and Morrey-Campanato Dirichlet Problems for Elliptic Systems in the Upper Half-Space

Potential Analysis - We prove well-posedness results for the Dirichlet problem in $mathbb {R}^{n}_{+}$ for homogeneous, second order, constant complex coefficient elliptic systems with boundary...     

On the Viscosity Solutions for Nonlinear Systems of Second Order Elliptic Equations

ＯｎｔｈｅＶｉｓｃｏｓｉｔｙＳｏｌｕｔｉｏｎｓｆｏｒＮｏｎｌｉｎｅａｒＳｙｓｔｅｍｓｏｆＳｅｃｏｎｄＯｒｄｅｒＥｌｉｐｔｉｃＥｑｕａｔｉｏｎｓＬｉｕＷｅｉａｎ（刘伟安）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ，Ｈｕｂｅｉ...     

Sign-Changing Solutions for a Class of Nonlinear Elliptic Problems

In the present paper,the author studies the existence of sign-changing solutions for nonlinear elliptic equations,which have jumping nonlinearities,and may or may not be resonant with respect to Fu(?)ik spectrum,via linking methods under Cerami condition.     

On Fixed Point and Almost Fixed Point Problems of Lower Semicontinuous Type Multivalued Mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.     

On Systems of Boundary Value Problems for Differential Inclusions

Herein we consider the existence of solutions to second-order, two-point boundary value problems （BVPs） for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.     

On Boundary Value Problems with the Shift for Nonlinear Elliptic Equations of Second Order

In this paper, we consider the boundary value problem with the shift for nonlinear uniformly elliptic equations of second order in a multiply connected domain,For this sake, we propose a modified boundary value problem for nonlinear elliptic systems of first order equations, and give a priori estimates of solutions for the modified boundary value problem. Afterwards we prove by using the Schauder fixedpoint theorem that this boundary value problem with some conditions has a solution. The result obtained is the generlization of the corresponding theorem on the Poincar boundary value problem.     

The Dirichlet Problem for a Class of Nonlinear Elliptic Equations

In this paper, we study the Dirichlet problem for the nonlinear an isotropic elliptic equation where is a bounded domain, m_i(i=1, 2, …, n) are positive integers, and a_(ij)(x)(i,j=1,2,…,n) are measurable functions on Ω. The Dirichlet problem for semilinear elliptic equation, (1) with m_i=1 (i=1,2,…, n), has been studied by several people, see e.g [1] and the bibliography in [1]. The general nonlinear problem(1) seems to be studied very little.     

On a Moser–Steffensen Type Method for Nonlinear Systems of Equations

Mediterranean Journal of Mathematics - This paper is devoted to the construction and analysis of a Moser–Steffensen iterative scheme. The method has quadratic convergence without evaluating...     

Structure of Coexistence States for a Class of Quasilinear Elliptic Systems

The structure of positive solutions of the p-Laplacian systems is discussed via bifurcation theory and monotone techniques.     

Optimal Hölder Continuity for a Class of Degenerate Elliptic Problems with an Application to Subsonic-Sonic Flows

In this paper, we first study a class of elliptic equations with anisotropic boundary degeneracy. Besides establishing the existence, uniqueness and comparison principle, we obtain the optimal Hölder estimates for weak solutions by the estimates in the Campanato space. Based on such Hölder estimates, we then investigate subsonic-sonic flows with singularities at the sonic curves in a symmetric convergent nozzle with straight wall for an approximate model of the potential flow equation. It is proved that the perturbation problem of the symmetric subsonic-sonic flow is solvable and the symmetric subsonic-sonic flow is stable.     

L~∞-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms

In this work,we will prove the existence of bounded solutions in W_0~(1,p)(Ω)∩L~∞(Ω) for nonlinear elliptic equations-div(a(x,u,▽u))+g(x,u,▽u)+H(x,▽u) =f,where a,g and H are Caratheodory functions which satisfy some conditions,and the right hand side/belongs to W~(-1,q)(Ω).     

Riemann—Hilbert Problem for the First Order Elliptic Systems

In this article we discuss the Riemann—Hilbert problems for the first order elliptic systems and prove the existence of the solution by means of general analytic function theory and Cauchy integral formula.     

On Scattering of Poles for Schr?dinger Operator from the Point of View of Dirichlet Series

In this article, we are concerned with the scattering problem of Schr?dinger operators with compactly supported potentials on the real line. We aim at combining the theory of Dirichlet series with scattering theory. New estimate on the number of poles is obtained under the situation that the growth of power series which is related to the potential is not too fast by using a classical result of Littlewood. We propose a new approach of Dirichlet series such that significant upper bounds and lower bounds on the number of poles are obtained. The results obtained in this paper improve and extend some related conclusions on this topic.