On Positive Multipeak Solutions of a Nonlinear Elliptic Problem |
| |
Authors: | Noussair, Ezzat S. Yan, Shusen |
| |
Affiliation: | School of Mathematics, University of New South Wales Sydney, NSW 2052, Australia School of Mathematics and Statistics, University of Sydney Sydney, NSW 2006, Australia |
| |
Abstract: | In this paper we continue our investigation in [5, 7, 8] onmultipeak solutions to the problem 2u+u=Q(x)|u|q2u, xRN, uH1(RN) (1.1) where = Ni=12/x2i is the Laplace operator in RN, 2 < q < for N = 1, 2, 2 < q < 2N/(N2) for N3, and Q(x)is a bounded positive continuous function on RN satisfying thefollowing conditions. (Q1) Q has a strict local minimum at some point x0RN, that is,for some > 0 Q(x)>Q(x0) for all 0 < |xx0| < . (Q2) There are constants C, > 0 such that |Q(x)Q(y)|C|xy| for all |xx0| , |yy0| . Our aim here is to show that corresponding to each strict localminimum point x0 of Q(x) in RN, and for each positive integerk, (1.1) has a positive solution with k-peaks concentratingnear x0, provided is sufficiently small, that is, a solutionwith k-maximum points converging to x0, while vanishing as 0 everywhere else in RN. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|