Solutions of elliptic problems of p-Laplacian type in a cylindrical symmetric domain

 http://repository.vnu.edu.vn/handle/VNU_123/27347

We consider the p-Laplacian type elliptic problem -div (a( x, del u)) = h(x)|u|(q-2)u + g(x) in Omega, u = 0 in partial derivative Omega, where O = Omega(1) x Omega(2).

RN is a bounded domain having cylindrical symmetry, O1.

Rm is a bounded regular domain and Omega(2) is a k-dimensional ball of radius R, centered in the origin and m + k = N, m >= 1, k >= 2.

Under some suitable conditions on the functions a and h, using variational methods we prove that the problem has at least one resp. at least two solutions in two cases: g = 0 and g not equal 0.

Title:	Solutions of elliptic problems of p-Laplacian type in a cylindrical symmetric domain
Authors:	N. T. Chung H. Q. Toan
Keywords:	elliptic problem p-Laplacian type cylindrical symmetric domain mountain pass theorem
Issue Date:	2012
Publisher:	SPRINGER, VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
Citation:	ISIKNOWLEDGE
Abstract:	We consider the p-Laplacian type elliptic problem -div (a( x, del u)) = h(x)|u|(q-2)u + g(x) in Omega, u = 0 in partial derivative Omega, where O = Omega(1) x Omega(2). RN is a bounded domain having cylindrical symmetry, O1. Rm is a bounded regular domain and Omega(2) is a k-dimensional ball of radius R, centered in the origin and m + k = N, m >= 1, k >= 2. Under some suitable conditions on the functions a and h, using variational methods we prove that the problem has at least one resp. at least two solutions in two cases: g = 0 and g not equal 0.
Description:	TNS06898 ; ACTA MATHEMATICA HUNGARICA Volume: 135 Issue: 1-2 Pages: 42-55 Published: APR 2012
URI:	http://repository.vnu.edu.vn/handle/VNU_123/27347 http://link.springer.com/article/10.1007/s10474-011-0163-6
ISSN:	0236-5294
Appears in Collections:	Bài báo của ĐHQGHN trong Web of Science