MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMSWITH SINGULARφ-LAPLACIAN

We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;）;, f ∈ C;（[0, ∞）, R), f′（u） > 0 for u > 0, and for some 0 < β < θ such that f（u） < 0 for u ∈ [0, β)（semipositone） and f（u） > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;（[0, β） ∪（β, ∞）, R),f′′（u） ≥ 0 for u ∈ [0, β) and f′′（u） ≤ 0 for u ∈（β, ∞）, then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.

NEUMANN PROBLEMS OF A CLASS OF ELLIPTIC EQUATIONS WITH DOUBLY CRITICAL SOBOLEV EXPONENTS

This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.

The Solvability of Neumann Problem for a Singular Parabolic Equation

The qualitative properties of solutions of a Neumann problem for the singular parabolic equation ut = （u^m-1 ux）x （-1 〈 m ≤0） is studied in this paper. It is proved that there exists a unique global smooth solution which depends on the initial value. The large time behavior of the solutions is also discussed.

ON NEUMANN PROBLEM FOR SOMESEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS

This paper is concerned with Neumann problem for semilinear elliptic equations involving Sobolev critical exponents with limit nonlinearity in boundary condition. By critical point theory and dual variational principle, the author obtains the existence and multiplicity results.

NEUMANN PROBLEM FOR THE LANDAU-LIFSHITZ-MAXWELL SYSTEM IN TWO DIMENSIONS

This paper is concerned with the global existence and the partial regularity for the weak solution of the Landau-Lifshitz-Maxell system in two dimensions with Neumann boundary conditions.

The Neumann Problem for Parabolic Hessian Quotient Equations

In this paper,we consider the Neumann problem for parabolic Hessian quotient equations.We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations.Also solutions of the classical Neumann problem converge to a translating solution.

Uniqueness and Radial Symmetry of Least Energy Solution for a Semilinear Neumann Problem

Consider the following Neumann problem d△u- u ＋ k（x）u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,where d 〉 0, B1 is the unit ball in R^N, k（x） = k（｜x｜） ≠ 0 is nonnegative and in C（-↑B1）, 1 〈 p 〈 N＋2/N-2 with N≥ 3. It was shown in [2] that, for any d 〉 0, problem （＊） has no nonconstant radially symmetric least energy solution if k（x） ≡ 1. By an implicit function theorem we prove that there is d0 〉 0 such that （＊） has a unique radially symmetric least energy solution if d 〉 d0, this solution is constant if k（x） ≡ 1 and nonconstant if k（x） ≠ 1. In particular, for k（x） ≡ 1, do can be expressed explicitly.

On a Critical Neumann Problem with a Perturbation of Lower Order

We investigate the solvability of the Neumann problem （1.1） involving the critical Sobolev nonlinearity and a term of lower order. We allow a coefficient of u in equation （1.1） to be unbounded. We prove the existence of a solution in a weighted Sobolev space.

New procedure to generate multipliers in complex Neumann problem and effective Kohn algorithm

The purpose of this paper is threefold.(i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of an example of Catlin-D'Angelo concerning the ineffectiveness of the latter.(ii) To extend the techniques of multiplier ideal sheaves for the complex Neumann problem to general systems of partial differential equations.(iii) To present a new procedure of generation of multipliers in the complex Neumann problem as a special case of the multiplier ideal sheaves techniques for general systems of partial differential equations.

TIME DOMAIN BOUNDARY ELEMENT METHODS FOR THE NEUMANN PROBLEM： ERROR ESTIMATES AND ACOUSTIC PROBLEMS

We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approxima- tions in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations ob- tained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.

Positive Solutions to a Neumann Problem of Semilinear Elliptic System with Critical Nonlinearity

In this paper, we consider the Neumann boundary value problem for a system of two elliptic equations involving the critical Sobolev exponents. By means of blowing-up method, we obtain behavior of positives with low energy and asymptotic behavior of positive solutions with minimum energy as the parameters λ,μ→∞.

The Neumann Problem for a Class of Fully Nonlinear Elliptic Partial Differential Equations

In this paper,we establish global C2 estimates to the Neumann problem for a class of fully nonlinear elliptic equations.As an application,we prove the existence and uniqueness of k-admissible solutions to the Neumann problems.

A NOTE ON THE C.NEUMANN PROBLEM

We prove that the C. Neumann problem in the case where the potential matrix A hasmultiple eigenvalues is completely integrable by means of the moment map and the confocalquadric.

Singularly perturbed Neumann problem for fractional Schrdinger equations

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrdinger equations with subcritical exponent. For some smooth bounded domain ? R^n, our boundary condition is given by∫_?u(x)-u(y)/|x-y|^(n+2s)dy = 0 for x ∈ R^n\?.We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on Rn.

The Neumann Problem of Complex Special Lagrangian Equations with Supercritical Phase

Inspired by the Neumann problem of real special Lagrangian equations with supercritical phase, we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper, and establish the global C^2 estimates and the existence theorem by the method of continuity.

NEUMANN PROBLEM FOR OVERDETERMINED SYSTEM RELATED WITH ALMOST COMPLEX STRUCTURE

In this paper we investigate an overdetermined system of differential equations, which is a generalization of both the Cauchy-Riemann equations and the Beltrami equation. The conditions under which the Neumann problem for the overdetermined system can be solved are given.

THE DIRICHLET PROBLEM AND NEUMANN PROBLEM FOR NONLINEAR PARABOLIC SYSTEMS OF SECOND ORDER EQUATIONS WITH MEASURABLE COEFFICIENTS IN A HIGHER DIMENSIONAL DOMAIN

In 1988, Yu . A. Alkhutov and I. T. Mamedov discussed the solvability of the Dirichlet problem for linear uniformly parabolic equations with measurable coefficients where the coefficients satisfy the condition In this paper, we try to generalize the results of Alkhutov and Mamedov to nonlinear uni- formly parabolic systems of second order equations with measurable coefficients; moreover, we also discuss the solvability of the Neumann problem for the above systems.

Existence of Solutions for p-Laplace Equations Subjected to Neumann Boundary Value Problem

The existence of solutions for one dimensional p-Laplace equation （φp（u′））′=f（t,u,u′） with t∈（0,1） and Фp（s）=｜s｜^p-2 s, s≠0 subjected to Neumann boundary value problem at u′（0） = 0, u′（1） = 0. By using the degree theory, the sufficient conditions of the existence of solutions for p-Laplace equation subjected to Neumann boundary value condition are established.

Localisation Inverse Problem and Dirichlet-to-Neumann Operator for Absorbing Laplacian Transport

We study Laplacian transport by the Dirichlet-to-Neumann formalism in isotropic media (γ = I). Our main results concern the solution of the localisation inverse problem of absorbing domains and its relative Dirichlet-to-Neumann operator . In this paper, we define explicitly operator , and we show that Green-Ostrogradski theorem is adopted to this type of problem in three dimensional case.

Neumann＇s method for boundary problems of thin elastic shells

The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.