On the Classification of Stable Solution to Biharmonic Problems in Large Dimensions
نویسندگان
چکیده
We give a new bound on the exponent for nonexistence of stable solutions to the biharmonic problem ∆u = u, u > 0 in R where p > 1, n ≥ 20.
منابع مشابه
Classification of the Stable Solution to Biharmonic Problems in Large Dimensions
We give a new bound on the exponent for the nonexistence of stable solutions to the biharmonic problem ∆u = u, u > 0 in R where p > 1, n ≥ 20.
متن کاملGENERAL SOLUTION OF ELASTICITY PROBLEMS IN TWO DIMENSIONAL POLAR COORDINATES USING MELLIN TRANSFORM
Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic ...
متن کاملExistence of at least one nontrivial solution for a class of problems involving both p(x)-Laplacian and p(x)-Biharmonic
We investigate the existence of a weak nontrivial solution for the following problem. Our analysis is generally bathed on discussions of variational based on the Mountain Pass theorem and some recent theories one the generalized Lebesgue-Sobolev space. This paper guarantees the existence of at least one weak nontrivial solution for our problem. More precisely, by applying Ambrosetti and Rabinow...
متن کاملElzaki transform method for finding solutions to two-dimensional elasticity problems in polar coordinates formulated using Airy stress functions
In this paper, the Elzaki transform method is used for solving two-dimensional (2D) elasticity problems in plane polar coordinates. Airy stress function was used to express the stress compatibility equation as a biharmonic equation. Elzaki transform was applied with respect to the radial coordinate to a modified form of the stress compatibility equation, and the biharmonic equation simplified t...
متن کاملLiouville theorems for stable Lane-Emden systems and biharmonic problems
We examine the elliptic system given by −∆u = v, −∆v = u, in R , (1) for 1 < p ≤ θ and the fourth order scalar equation ∆u = u, in R , (2) where 1 < θ. We prove various Liouville type theorems for positive stable solutions. For instance we show there are no positive stable solutions of (1) (resp. (2)) provided N ≤ 10 and 2 ≤ p ≤ θ (resp. N ≤ 10 and 1 < θ). Results for higher dimensions are also...
متن کامل