# ON A SINGULAR SUBLINEAR POLYHARMONIC PROBLEM

## Related Articles

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We will study the following polyharmonic nonlinear elliptic equation (-Î”)mu + f (Â·,u)= 0 in â„n, n > 2m. Under appropriate conditions on the nonlinearity f (x, t), related to a class of functions called m-Green-tight functions, we give some existence results for the above equation.

- EXISTENCE OF POSITIVE SOLUTIONS FOR SOME NONLINEAR ELLIPTIC PROBLEMS IN UNBOUNDED DOMAINS OF Rn. Zeddini, Noureddine // Abstract & Applied Analysis;2006, p1
This paper deals with a class of nonlinear elliptic equations in an unbounded domain D of â„n, n â‰¥ 3, with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class Kâˆž(D). Our purpose is to give some existence...

- Correctness of the Dirichlet problem for the Lavrent'ev-Bitsadze equation. Aldashev, Serik // Journal of Mathematical Sciences;Jan2013, Vol. 188 Issue 2, p71
It is shown that the Dirichlet problem in a multidimensional domain for the Lavrent'ev-Bitsadze equation is uniquely solvable. A criterion of the uniqueness of the solution is obtained.

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We will be concerned with the existence result of unilateral problem associated to the equations of the form Au + g(x,u, âˆ‡u) = f , where A is a Leray-Lions operator from its domain D(A) âŠ‚ W0Â¹ LM(Î©) into W-1EM(Î©). On the nonlinear lower order term g(x,u, âˆ‡u), we assume...

- Adaptive Bidirectional Flow for Image Interpolation and Enhancement. Shujun Fu; Qiuqi Ruan; Wenqia Wang // International Journal of Information Technology;2006, Vol. 2 Issue 4, p288
Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually the effects of blurred edges and jagged artifacts in the image to some extent. This paper presents an adaptive feature preserving bidirectional flow process, where...

- Application of Maslov’s formula to finding an asymptotic solution to an elastic deformation problem. Kostin, D. V. // Mathematical Notes;Feb2008, Vol. 83 Issue 1/2, p48
We propose a scheme of bifurcation analysis of equilibrium configurations of a weakly inhomogeneous elastic beam on an elastic base under the assumption of two-mode degeneracy; this scheme generalizes the Darinskii-Sapronov scheme developed earlier for the case of a homogeneous beam. The...

- Global Optimal Regularity for the Parabolic Polyharmonic Equations. Fengping Yao // Boundary Value Problems;2010, Special section p1
We show the global regularity estimates for the following parabolic polyharmonic equation ut(-Î”)m u = f in Rn x (0, âˆž), m âˆˆ â„¤+ under proper conditions. Moreover, it will be verified that these conditions are necessary for the simplest heat equation ut - Î”u = f in Rn x (0,...

- A boundary value problem with conditions on the entire boundary of a noncharacteristic domain for a fourth-order equation. Utkina, E. A. // Doklady Mathematics;Aug2011, Vol. 84 Issue 1, p539
The article presents a methodology for obtaining conditions in order to derive a unique solution for a Dirichlet problem involving a pseudoparabolic equation. It notes that the proposed methodology employs the reduction of the problem to Fredholm integral equations wherein the unique solvability...

- A nonlocal boundary value problem for the Lavrent'ev-Bitsadze equation. Moiseev, E.; Likhomanenko, T. // Doklady Mathematics;Sep2012, Vol. 86 Issue 2, p635
The article focuses on nonlocal boundary value problems for the Lavrent'ev-Bitsadze equation in two- and three-dimensional cases. It notes that the dirichlet problem is solvable if a countable set of orthogonality is provided on the sight-hand side of the nonlocal condition for some other values...