Recurrence Relations between Solutions of Some Elliptic Problems in < n and
نویسنده
چکیده
i=1 (∆− μiI)vk = h(x), x ∈ <+, μi > 0, ( ∂vi ∂xn + snvi)xn=0 = φi(x ′ ), x ′ = (x1, ...xn−1) ∈ a; and we obtain for h(x)≡ 0 a relation between the inverse Laplace transforms v k,2m(x ′ , sn) and solutions of a similar problem to (1) in x ′ ∈ 0 instead of μi, and then using inverse tabular transform , we find explicit formula for the solution v1,2(x).
منابع مشابه
Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces
The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega, $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...
متن کاملRecurrence and Asymptotic Relations of a Generalized Elliptic-type Integral
Epstein-Hubbell 1963 elliptic-type integrals occur in radiation field problems. In this paper, we consider a generalization of the elliptic-type integrals introduced by Kalla and Tuan 1996 and developed by Salman 2006. We give some recurrence relations for this generalized special function. Some of these relations can be used for analytic continuation to different domains. Asymptotic relations ...
متن کاملA two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملHigher Order Moments and Recurrence Relations of Order Statistics from the Exponentiated Gamma Distribution
Order statistics arising from exponentiated gamma (EG) distribution are considered. Closed from expressions for the single and double moments of order statistics are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic for different choices of r, n and /theta are presented. Recurrence relations between single and double moments of r...
متن کاملNew conditions on ground state solutions for Hamiltonian elliptic systems with gradient terms
This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...
متن کامل