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一类半线性抛物型方程的Liouville型定理 被引量：1

Liouville type theorem of a class of semilinear parabolic equations
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摘要 受Birindelli等研究散度型算子的半线性方程的Liouville型问题的思想的启发,结合Laptev等构造试验函数的方法,本文首先构造一类特殊的试验函数,结合其性质对泛函进行精确估计,进而给出一类半线性抛物型方程的Liouville型定理. Inspired by the thought of Birindelli etc. who studied the Liouville type problem of semilinear equations with divergence type operators, combined the method of Laptev who constructed test functions, we coustruct a class of special test functions firstly. Then we estimate accurately the functional with some properties of test functions, and give the Liouville type theorem of a class of semilinear parabolic equations.
作者 张书陶 李状君
机构地区 中国计量学院数学系
出处 《西南民族大学学报（自然科学版）》 CAS 2007年第6期1269-1273,共5页 Journal of Southwest Minzu University(Natural Science Edition)
基金 浙江省自然科学基金资助(项目编号为Y606144).
关键词 LIOUVILLE型定理 半线性抛物方程 Liouville type theorem semilinear parabolic equation
分类号 O175.26 [理学—基础数学]
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参考文献10

  • 1BWEWATYCKI H, CAPUZZO DOLCETTA I, NIRENBERG. L. Problemes elliptiques indefinites et theo- rems de Liouville non-lineaires[J]. C. R. Acad. Sci. Paris, Seris I, 1993, 317: 945-950.
  • 2BERESTYCKI H, CAPUZZO DOLCETTA I, NIRENBERG L. Superlinear indefinite elliptic problems and nonlinear Liouville theorems[J]. Topological Methods in Nonlinear Analysis, 1994, 414: 59-78,
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同被引文献9

  • 1Berestycki H, Dolcetta I C, Nirenberg L. Superlinear Indefinite Elliptic Problems and Nonlinear Liouville Theorems[J]. Topological Methods in Nonlinear Analysis, 1994,4(1) :59.
  • 2Birindelli I,Dolcetta I C,Cutri A. Liouville Theorems for Semilinear Equationgs on the Heisenberg Group [J]. Ann Inst H Poineare Anal Non Lineaite, 1997, 14(3).295.
  • 3Birindelli I,Dolcetta I C,Cutri A. Indefinite Semi-linear Equations on the Heisenberg Group: A Priori Bounds and Existence[J]. Comm in P D E, 1998,23 (7/8):1123.
  • 4Mitidieri E, Pohozaev S I. Nonexistence of Positive Solutiongs for a Systems of Quasilinear Elliptic E- quations and Inequalinties in R^n[J]. Doklady Mathematics, 1999,59(3) : 351.
  • 5Mitidieri E, Pohozaev S I. Nonexistence of Positive Solutions for Quasilinear Elliptic Problems on R^n[J]. Proceedings of the Steklov Mathematical Institute,1999,227:1.
  • 6Mitidieri E, Pohozaev S I. Nonexistence of Weak Solutions for Some Degenerate and Singular Hyperbolic Problems on R^n+1 [J]. Proceedings of the Steklov Mathematical Institute, 2001,232 : 240.
  • 7Mitidieri E, Pohozaev S I. Nonexistence of Weak Solutions for Some Degenerate Elliptic and Parabolic Problems on R^n [J]. Journal of Evolution Equations, 2001,1 : 189.
  • 8Hamidi A E, Laptev G G. Nonexistence of Solutions to Systems of Higher-order Semilinear Inequalities in Cone-like Domains[J/OL], Electronic J. Differential Equations,2002, 2002 (97) :1. [2002-11-14]. URL: http://ejde, math. unt. edu/.
  • 9Laptev G G. Nonexistence Results for Higher-order Evolution Partial Differential Inequalities[J]. Proc Amer Math Soc, 2002,131: 415.

引证文献1

西南民族大学学报（自然科学版）
2007年 第6期

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