圆锥区域中变系数半线性抛物型微分不等式的刘维尔型定理Liouville Theorems of Semi-linear Parabolic Differential Inequalities with Variable Coefficients in Cone
方钟波,付超
摘要(Abstract):
研究圆锥区域中变系数半线性抛物型微分不等式及其耦合不等式组的刘维尔型定理。先给出弱解的定义,再利用构造试验函数法建立不依赖于初始值的解的universal估计,最后得到非负非平凡整体弱解的在适当的临界指数范围内不存在的结论,此种方法的主要特点是不用比较原理和极值原理。
关键词(KeyWords): 微分不等式;试验函数;刘维尔型定理
基金项目(Foundation): 国家留学回国人员科研启动基金项目(910937020)资助
作者(Author): 方钟波,付超
DOI: 10.16441/j.cnki.hdxb.2012.04.015
参考文献(References):
- [1]Berestycki H,Capuzzo Dolcetta I,Nirenberg L.Superlinear in-denite elliptic problems and nonlinear Liouville theorems[J].Topol Methods Nonlinear Anal,1994,1:59-78.
- [2]Birindelli I,Demengel F.Some Liouville theorems for the p-Lapla-cian[J].Elec J Differential Equations,Conference,2002,8:35-46.
- [3]Birindelli I,Mitidieri E.Liouville theorems for elliptic inequalitiesand applications[J].Proc Royal Soc Edinburgh,1998,128:1217-1247.
- [4]Dancer E N,Du Y.Some remarks on liouville type results for qua-si-linear elliptic equations[J].Proc Amer Math Soc,2002,131:1891-1899.
- [5]Kartsatos A G,Kurta V V.On the critical Fujita exponents forsolutions of quasilinear parabolic inequalities[J].J Math AnalAppl,2002,269:73-86.
- [6]Piccirillo A M,Toscano L,Toscano S.Blow-up results for a classof first-order nonlinear evolution inequalities[J].J Differential E-quations,2005,212:319-350.
- [7]Fujita H.On the blowing up of solutions to the Cauchy problem for ut=Δu+u1+α[J].J Fac Sci Univ Tokyo Sect,1966,13:119-124.
- [8]Hayakawa K.On nonexistence of global solution of some semilin-ear parabolic differential equations[J].Proc Japan Acad Ser A,1979,49:503-505.
- [9]Mitidieri E,Pohozaev S L.A priori estimates and blow-up of solu-tions to non-linear partial differential equations and inequalities[J].Proc Steklov Inst Math,2001,234:1-383.
- [10]Kondratev V A.Boundary-value problems for elliptic equationsin domains with conic and angular points[J].Trans MoscowMath Soc,1967,16:209-292.
- [11]Bonfiglioli A,Lanconelli E.Liouville-type theorems for real sub-Laplacians[J].Manuscripta Math,2001,105:111-124.
- [12]Laptev G G.Non-existence of solutions of semilinear parabolicdierential inequalities in cones[J].Matematicheskii Sbornik,2001,192:51-70.
- [13]Marco Rigoli,Alberto G Setti.A Liouville theorem for a class ofsuperlinear elliptic equations on cones[J].Nonlinear dier equ ap-pl,2002,9:15-36.
- [14]Tomomitsu Teramoto,Hiroyuki Usami.A liouville type theoremfor semiliear elliptitc systems[J].Pacific Journal of Mathemat-ics,2002,204:247-255.
- [15]Bandle C,Essen M.On positive solutions of Emden equations incone-like domains[J].Arch Rational Mech Anal,1990,4:319-338.
- [16]Laptev G G.Absence of solutions to semilinear parabolic differ-ential inequalities in cones[J].Mat Sb,2001,192:51-70.
- [17]Laptev G G.Nonexistence of Solutions of Elliptic Dierential Inequali-ties in Conic Domains[J].Mat Zametki,2002,71(6):855-866.
- [18]Caristi G.Existence and nonexistence of global solutions of de-generate and singular parabolic systems[J].Abstr Appl Anal,2000,5:265-284.
文章评论(Comment):
|
||||||||||||||||||
|
||||||||||||||||||