Open Access

Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

Boundary Value Problems20072007:016407

DOI: 10.1155/2007/16407

Received: 29 June 2006

Accepted: 17 October 2006

Published: 9 January 2007

Abstract

We consider the problem https://static-content.springer.com/image/art%3A10.1155%2F2007%2F16407/MediaObjects/13661_2006_Article_634_IEq1_HTML.gif where https://static-content.springer.com/image/art%3A10.1155%2F2007%2F16407/MediaObjects/13661_2006_Article_634_IEq2_HTML.gif is not identically zero. Under the condition that https://static-content.springer.com/image/art%3A10.1155%2F2007%2F16407/MediaObjects/13661_2006_Article_634_IEq3_HTML.gif satisfies (H), we show that there exists https://static-content.springer.com/image/art%3A10.1155%2F2007%2F16407/MediaObjects/13661_2006_Article_634_IEq4_HTML.gif such that the above-mentioned equation admits at least one solution for all https://static-content.springer.com/image/art%3A10.1155%2F2007%2F16407/MediaObjects/13661_2006_Article_634_IEq5_HTML.gif . This extends the results of Laplace equation to the case of https://static-content.springer.com/image/art%3A10.1155%2F2007%2F16407/MediaObjects/13661_2006_Article_634_IEq6_HTML.gif -Laplace equation.

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Authors’ Affiliations

(1)
Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University

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Copyright

© Z. Yang and B. Xu 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.