# ESTIMATES FOR THE GREEN FUNCTION AND EXISTENCE OF POSITIVE SOLUTIONS FOR HIGHER-ORDER ELLIPTIC EQUATIONS

## Related Articles

- Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem. Chenghua Gao // Abstract & Applied Analysis;2012, p1
This paper is concerned with the existence of solutions for the discrete second-order boundary value problem Î”2u(t - 1) + Î» 1u(t) + g(Î”u(t)) = f(t), tÎµ{1,2,...,T}, u(0) = u(T + 1) = 0, where T > 1 is an integer, f : {1,...,T} âž™ R, g : R âž™ R is bounded and continuous,...

- Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem. Ma, Ruyun; Yanqiong Lu // Abstract & Applied Analysis;2012, p1
we show the existence and multiplicity of positive solutions of the nonlinear discrete fourth-order boundary value problem Î”4u(t - 2) = Î»h(t) f (u(t)), t Îµ T2, u(1) = u(T + 1) = Î”2u(0) = Î”2u(T) = 0, where Î» > 0, h : T2 --Â» (0,âˆž) is continuous, and f : R...

- Some Aspects of the Boundary Trace Problem for Solutions of Nonlinear Elliptic Equations. Véron, Laurent // Journal of Mathematical Sciences;Dec2004, Vol. 124 Issue 4, p5163
The boundary trace problem for positive solutions of -Î”u + g(x, u) = 0 is considered for a large class of nonlinearities and three different methods for defining the trace are compared. The boundary trace is usually a generalized Borel measure. The associated Dirichlet problem with boundary...

- ON THE RATE OF THE VOLUME GROWTH FOR SYMMETRIC VISCOUS HEAT-CONDUCTING GAS FLOWS WITH A FREE BOUNDARY. Zlotnik, Alexander // Abstract & Applied Analysis;2006, p1
The system of quasilinear equations for symmetric flows of a viscous heat-conducting gas with a free external boundary is considered. For global in time weak solutions having nonstrictly positive density, the linear in time two-sided bounds for the gas volume growth are established.

- The Use of Phase-Lag and Amplification Error Integrators for the Numerical Solution of the Radial SchrÃ¶dinger Equation. Papadopoulos, D. F.; Anastassi, Z. A.; Simos, T. E. // AIP Conference Proceedings;9/30/2010, Vol. 1281 Issue 1, p1839
A new numerical method is developed, based on the combination of the nullification of the phase-lag and the amplification factor, along with the nullification of their antiderivatives.

- Numerical analysis of reversible A ... B ... C reaction-diffusion systems. Koza, Z. // European Physical Journal B -- Condensed Matter;Apr2003, Vol. 32 Issue 4, p507
: We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B â†” C with initially separated reactants. Using it we find that there are three types of asymptotic reaction zones. In particular we show that the reaction...

- Dynamics of Model Error: The Role of the Boundary Conditions. Nicolis, C. // Journal of the Atmospheric Sciences;Jan2007, Vol. 64 Issue 1, p204
The different modes of the early stages of the response of a forecasting model to a small error in the boundary conditions are analyzed. A general formulation of the problem based on the use of Greenâ€™s functions is developed and implemented on systems in which the operators acting on the...

- CPIM-Improved Meshless Method for Engineering Application. Tsai, M. C.; Lee, H. H.; Chang, P.-Y. // AIP Conference Proceedings;5/21/2010, Vol. 1233 Issue 1, p1395
To improve the application of Point Interpolation Method (PIM) in Element Free Galerkin Method (EFG) is the aim of this study. The trait of EFG is using overlap of influence domain between different nodes to construct discretization nodesâ€™ connection. EFG just uses nodal data, but not...

- Dirichlet problems for harmonic maps from regular domains. Bent Fuglede // Proceedings of the London Mathematical Society;Jul2005, Vol. 91 Issue 1, p249
Given an open set $\Omega$ of compact closure in $\mathbb{R}^m$, the classical Dirichlet problem is to extend a given continuous function $\psi : \partial \Omega \to \mathbb{R}$ to a continuous function $\phi : \overline \Omega \to \mathbb{R}$ such that $\phi$ is harmonic (that is, satisfies the...