Open Access

Multiple Positive Solutions for a Class of Concave-Convex Semilinear Elliptic Equations in Unbounded Domains with Sign-Changing Weights

Boundary Value Problems20102010:856932

DOI: 10.1155/2010/856932

Received: 8 September 2010

Accepted: 18 October 2010

Published: 21 October 2010

Abstract

We study the existence and multiplicity of positive solutions for the following Dirichlet equations: https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq1_HTML.gif in https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq2_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq3_HTML.gif on https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq4_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq5_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq6_HTML.gif ( https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq7_HTML.gif if https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq8_HTML.gif ; https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq9_HTML.gif if https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq10_HTML.gif ), https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq11_HTML.gif is a smooth unbounded domain in https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq12_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq13_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq14_HTML.gif satisfy suitable conditions, and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq15_HTML.gif maybe change sign in https://static-content.springer.com/image/art%3A10.1155%2F2010%2F856932/MediaObjects/13661_2010_Article_959_IEq16_HTML.gif .

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Authors’ Affiliations

(1)
Center for General Education, Chang Gung University

Copyright

© Tsing-San Hsu. 2010

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.