báo cáo hóa học:" Research Article Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 845946 16 pages doi 2009 845946 Research Article Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms C. A. Santos Department of Mathematics University of Brasilia 70910-900 Brasilia DF Brazil Correspondence should be addressed to C. A. Santos csantos@ Received 31 May 2009 Revised 13 August 2009 Accepted 2 October 2009 Recommended by Wenming Zou 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 -ApU afx f u Xb x g u x e RN 1 p N where f g 0 to 0 to are suitable functions and afx 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 0 A A for some A 0. Penalty arguments variational principles lower-upper solutions and an approximation procedure will be explored. 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. 1. Introduction In this paper we establish new results concerning existence and behavior at infinity of solutions for the nonlinear quasilinear problem -ApU a x f u Ab x g u in RN u 0 in RN u x 0 x to where Apu div Vu p-2Vu with 1 p N denotes the p-Laplacian operator a b RN 0 to and f g 0 to 0 to are continuous functions not identically zero and A 0 is a real parameter. A solution of is meant as a positive function u e C1 RN with u x 0 as x to and Vu p 2VúVydx a x f u Ab x g u ydx Vy e Cto rn - RN RN 2 Boundary Value Problems The class of problems appears in many nonlinear phenomena for instance in the theory of quasiregular and quasiconformal mappings 1-3 in the generalized reaction-diffusion theory 4 in the .

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