Local superlinearity and sublinearity for indefinite semilinear elliptic problems

被引：175

作者：

De Figueiredo, DG

Gossez, JP

Ubilla, P

机构：

[1] Free Univ Brussels, Dept Math, B-1050 Brussels, Belgium

[2] UNICAMP, IMECC, BR-13081970 Campinas, SP, Brazil

[3] Univ Santiago Chile, Dept Matemat, Santiago, Chile

[4] Univ Santiago Chile, CC, Santiago, Chile

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2003年 / 199卷 / 02期

关键词：

superlinearity; sublinearity; indefinite nonlinearity; concave-convex nonlinearity; semilinear elliptic problem;

D O I：

10.1016/S0022-1236(02)00060-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper the usual notions of superlinearity and sublinearity for semilinear problems like -Deltau =f (x, u) are given a local form and extended to indefinite nonlinearities. Here f (x, s) is allowed to change sign or to vanish for s near zero as well as for s near infinity. Some of the well-known results of Ambrosetti-Brezis-Cerami are partially extended to this context. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：452 / 467

页数：16

共 12 条

[1] Inhibition of DNA polymerase alpha expression and cell growth, a possible triple helix mechanism
Alama, A
Barbieri, F
Cagnoli, M
Mazzei, M
Grandi, T
Nicolin, A
[J]. ANTISENSE & NUCLEIC ACID DRUG DEVELOPMENT, 1996, 6 (02): : 95 - 101
[2] ON SEMILINEAR ELLIPTIC-EQUATIONS WITH INDEFINITE NONLINEARITIES
ALAMA, S
TARANTELLO, G
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1993, 1 (04) : 439 - 475
[3] Elliptic problems with nonlinearities indefinite in sign
Alama, S
Tarantello, G
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 141 (01) : 159 - 215
[4] COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS
AMBROSETTI, A
BREZIS, H
CERAMI, G
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (02) : 519 - 543
[5] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[6] BERESTYCKI H, 1995, NODEA-NONLINEAR DIFF, V2, P533
[7] VARIATIONAL ELLIPTIC PROBLEMS WHICH ARE NONQUADRATIC AT INFINITY
COSTA, DG
MAGALHAES, CA
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (11) : 1401 - 1412
[8] ON PAIRS OF POSITIVE SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC PROBLEMS
DEFIGUEIREDO, DG
LIONS, PL
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1985, 34 (03) : 591 - 606
[9] Gilbar D., 1983, ELLIPTIC PARTIAL DIF
[10] Grisvard P., 1985, ELLIPTIC PROBLEMS NO, V24

← 1 2 →