摘要
本文研究奇异椭圆方程的边值问题.利用变分方法和锥理论中的混合单调方法,证明了奇异方程正解的存在性。
出处
《数学年刊(A辑)》
CSCD
北大核心
2000年第4期427-436,共10页
Chinese Annals of Mathematics
参考文献17
-
1[1]Crandall, M. G., Rabinowitz, P. H. & Tartar, L. On a Dirichlet problem with a singular nonlinearity [J], Comm. Partial Differential Equations, 2:2(1977),193--222
-
2[2]Usami, H. On a singular elliptic boundary value problem in a ball [J], Nonlinear Anal., 13:10(1989),1163--1170
-
3[3]Gomes, S. M. On a singular nonlinear elliptic problem [J], SIAM J. Math. Anal., 17:6(1986),1359--1369
-
4[4]Lair, A. V. & Shaker, A. W. Classical and weak solutions of singular semilinear ellipticproblem [J], J. Math. Anal. Appl., 211(1997),371--385
-
5[5]Edelson, A. Entire solution of singular elliptic equations [J], J. Math. Anal. Appl., 139(1989),523--532
-
6[6]Lazer, A. C. & Mckenna, P. J. On a singular nonlinear elliptic boundary value problem [J], Proc. Amer. Math. Soc., 111(1991),721--730
-
7[7]Struwe, M. Variational method [M], Springer-Verlag, New York, 1990
-
8[8]Lair, A. V. & Shaker, A. W. Entire solution of a singular semilinear elliptic problem[J], J. Math. Anal. Appl., 200(1996),498--505
-
9[9]Kusano, T. & Swanson, A. Entire positive solutions of a singular semilinear ellipticequations [J], Japan J. Math.(N.S.), 11:1(1985), 145--155
-
10[10]Shaker, A. W. On singular semilinear elliptic equations [J], J. Math. Anal. Appl., 173(1993),222--228
同被引文献17
-
1梁学信.一类半线性抛物型方程组解的blow-up[J].应用数学学报,1997,20(1):146-150. 被引量:1
-
2叶其孝 李正元.反映扩散方程引论[M].北京:科学出版社,1990..
-
3Crandall M G, Rabinowitz P H, Tartar L. On a Dirichlet problem with a singular nonlinearity[ J ]. Commun Part Diff E qns, 1977, 2(2) :193 -222.
-
4Lazer A C, Mckenna P J. On a singular nonlinear elliptic boundary- value problem [ J]. Proc Am Math Soc, 1991,111:721 -730.
-
5Lair A V, Shaker A W. Classical and weak solutions of a singular semilinear elliptic problem [ J ]. J Math Anal Appl, 1997,211 : 371 - 385.
-
6Sun Y J, Wu S P, Long Y M. Combined effects of singular and superlinear non - linearities in some singular boundary value prob- lems[J]. J DiffEqns,2001,176:511-531.
-
7Yang H T. Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem [ J ]- J Diff Eqns, 2003,189:487 - 512.
-
8Hirano N, Saccon C, Shioji N. Brezis - Nirenberg type theorems and muhiplieity of positive solutions for a singular elliptic prob- lem [ J ]. J Diff Eqns,2008,245 : 1997 - 2037.
-
9Sun Y J, Wu S P. An exact estimate result for a class of singular equations with critical exponents[ J]. J Funct Anal 2011,260: 1257 - 1284.
-
10Boccardo L. A Dirichlet problem with singular and supereritieal nonlinearities [ J ]. Nonlinear Anal,2012,75:4436 -4440.
二级引证文献3
-
1刘玉清.一类退化方程组解的爆破[J].江苏工业学院学报,2006,18(2):59-60.
-
2廖家锋,陈明,张鹏.一类奇异Kirchhoff型问题正解的存在性[J].四川师范大学学报(自然科学版),2016,39(1):103-106. 被引量:6
-
3李红英,佘连兵,廖家锋.一类奇异p-Laplace方程正解的存在性[J].西北师范大学学报(自然科学版),2016,52(4):1-4. 被引量:1
-
1韩彦武,钮鹏程.二阶奇异椭圆方程的Dirichlet问题[J].纯粹数学与应用数学,2004,20(1):29-34. 被引量:1
-
2吴建华,李艳玲.非线性微分方程(组)的单调方法[J].纺织高校基础科学学报,1996,9(3):229-232. 被引量:1
-
3元春梅,徐本龙,许友军.一类奇异椭圆方程正解存在性[J].工程数学学报,2005,22(3):551-554.
-
4肖建海,侯焱华.关于奇异椭圆方程的研究(英文)[J].孝感学院学报,2004,24(3):51-54.
-
5夏莉,姚正安,周文书.一类非线性奇异椭圆方程的非平凡解[J].数学年刊(A辑),2008,29(1):15-26. 被引量:2
-
6韩国强.一类奇异方程两点边值问题的差分—样条校正解[J].计算数学,1991,13(2):187-192. 被引量:1
-
7唐鸣放.一类双曲型拟线性奇异方程的Cauchy问题[J].重庆建筑工程学院学报,1990,12(2):92-99.
-
8王远弟.关于一个奇异方程的边值问题[J].贵州大学学报(自然科学版),1994,11(2):78-80.
-
9李林.奇异Lienard方程的极限环[J].纯粹数学与应用数学,1992,8(2):54-59.
-
10胡丽平.带有Sobolev临界指数的奇异椭圆方程的解(英文)[J].河南科学,2006,24(4):469-473. 被引量:1