Boundary Value Problems
Volume 2009 (2009), Article ID 845946, 16 pages
Research Article

Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms

Department of Mathematics, University of Brasília, 70910–900 Brasília, DF, Brazil

Received 31 May 2009; Revised 13 August 2009; Accepted 2 October 2009

Academic Editor: Wenming Zou

Copyright © 2009 C. A. Santos. 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.


We establish new results concerning existence and asymptotic behavior of entire, positive, and bounded solutions which converge to zero at infinite for the quasilinear equation Δpu=a(x)f(u)+λb(x)g(u),  xN,  1<p<N, where f,g:[0,)[0,) are suitable functions and a(x),b(x)0 are not identically zero continuous functions. We show that there exists at least one solution for the above-mentioned problem for each 0λ<λ, for some λ>0. Penalty arguments, variational principles, lower-upper solutions, and an approximation procedure will be explored.