An Application of a Mountain Pass Theorem
查看参考文献13篇
|
文摘
|
We are concerned with the following Dirichlet problem: where f(x,t) ∈ C((Ω-bar)*R), f(x,t)/t is nondecreasing in t ∈ R and tends to an L~∞-function q(x) uniformly in x ∈ Ω as t → + ∞ (i.e., f(x,t) is asymptotically linear in t at infinity). In this case, an Ambrosetti-Rabinowitz-type condition, that is, for some θ > 2, M > 0, 0 < θF(x, s) ≤ f(x,s)s, for all |s| ≥ M and x ∈ Q, (AR) is no longer true, where F(x,s) = ∫from x=0 to x=s of f(x,t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming (AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable conditions on f(x,t) and q(x). Our methods also work for the case where f(x,t) is superlinear
in t at infinity, i.e., q(x) = +∞. |
|
来源
|
Acta Mathematica Sinica. English Series
,2002,18(1):27-36 【核心库】
|
|
DOI
|
10.1007/s101140100147
|
|
关键词
|
Dirichlet problem
;
Mountain Pass Theorem
;
Asymptotically linear
;
Resonant problem
|
|
地址
|
中科院武汉物理与数学所, Laboratory of Mathematical Physics, CAS, Wuhan, 430071
|
|
语种
|
英文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
1439-8516 |
|
学科
|
数学 |
|
文献收藏号
|
CSCD:1492242
|
参考文献 共
13
共1页
|
|
1.
Ambrosetti A.
J. Funct. Anal,1973,14:349-381
|
CSCD被引
203
次
|
|
|
|
|
2.
Rabinowitz P H.
Amer. Math. Soc,1986
|
CSCD被引
3
次
|
|
|
|
|
3.
Brezis H.
Comm. Pure Appl. Math,1983,36:437-477
|
CSCD被引
202
次
|
|
|
|
|
4.
Costa D G.
Nonli. Anal. TMA,1994,23:1401-1412
|
CSCD被引
26
次
|
|
|
|
|
5.
Jeanjean L.
Proc. Royal. Soc. Edinburgh, Section A,1999,129:787-809
|
CSCD被引
37
次
|
|
|
|
|
6.
Schechter M.
Manuscripta Math,1995,86:253-265
|
CSCD被引
7
次
|
|
|
|
|
7.
Stuart C A.
Math. Methods in Applied Sciences,1996,19:1397-1407
|
CSCD被引
10
次
|
|
|
|
|
8.
Stuart C A.
Comm. in PDE,1999,24:1731-1758
|
CSCD被引
13
次
|
|
|
|
|
9.
Costa D G.
J. Math. Anal. Applications,1995,193:77-755
|
CSCD被引
1
次
|
|
|
|
|
10.
Mawhin J.
Arch. Rat. Mech. Anal,1986,95:269-277
|
CSCD被引
3
次
|
|
|
|
|
11.
Ekeland I.
Convexity Methods in Hamiltonian Mechanics,1990
|
CSCD被引
36
次
|
|
|
|
|
12.
Schechter M.
J. London Math. Soc,1991,44(2):491-502
|
CSCD被引
18
次
|
|
|
|
|
13.
Evans L C.
AMS,1997:19
|
CSCD被引
1
次
|
|
|
|
|
了解气象卫星更多信息，请访问